0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.06 % Command : run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.14/0.42 % Computer : n003.cluster.edu 0.14/0.42 % Model : x86_64 x86_64 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz 0.14/0.42 % Memory : 8046.5625MB 0.14/0.42 % OS : Linux 6.8.0-71-generic 0.14/0.42 % CPULimit : 1440 0.14/0.42 % WCLimit : 180 0.14/0.42 % DateTime : Mon Jul 27 13:31:23 UTC 2026 0.14/0.42 % CPUTime : 0.14/0.42 Running run_E /export/starexec/sandbox/benchmark/theBenchmark.p 180 THM 0.14/0.49 Running higher-order theorem proving 0.24/0.54 Running: /export/starexec/sandbox/solver/bin/eprover-ho --delete-bad-limit=2000000000 --definitional-cnf=24 -s --print-statistics -R --print-version --proof-object --auto-schedule=8 --cpu-limit=180 /export/starexec/sandbox/tmp/tmp.BWUfY4Bu2F/E---3.1_4003794.p 0.29/0.89 % Version: 3.5.1-ho 0.29/0.89 % partial match(1): HSLMSLSMSSSNHSA 0.29/0.89 % Preprocessing class: HSLMSLSSSSSNHSA. 0.29/0.89 % Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.29/0.89 % Starting new_ho_10 with 360s (2) cores 0.29/0.89 % Starting sh3 with 360s (2) cores 0.29/0.89 % Starting ho_unfolding_3 with 360s (2) cores 0.29/0.89 % Starting new_ho_10_cnf2 with 360s (2) cores 0.29/0.89 % new_ho_10 with pid 4003807 completed with status 0 0.29/0.89 % Result found by new_ho_10 0.29/0.89 % partial match(1): HSLMSLSMSSSNHSA 0.29/0.89 % Preprocessing class: HSLMSLSSSSSNHSA. 0.29/0.89 % Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.29/0.89 % Starting new_ho_10 with 360s (2) cores 0.29/0.89 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto) 0.29/0.89 % No SInE strategy applied 0.29/0.89 % Search class: HGHSM-SMLM31-MHSFFMBN 0.29/0.89 % partial match(1): HGHSM-SMLM31-MHSFFSBN 0.29/0.89 % Scheduled 5 strats onto 2 cores with 360 seconds (360 total) 0.29/0.89 % Starting SubtermCWHack with 37s (1) cores 0.29/0.89 % Starting new_ho_10 with 217s (1) cores 0.29/0.89 % new_ho_10 with pid 4003814 completed with status 0 0.29/0.89 % Result found by new_ho_10 0.29/0.89 % partial match(1): HSLMSLSMSSSNHSA 0.29/0.89 % Preprocessing class: HSLMSLSSSSSNHSA. 0.29/0.89 % Scheduled 4 strats onto 8 cores with 180 seconds (1440 total) 0.29/0.89 % Starting new_ho_10 with 360s (2) cores 0.29/0.89 % (lift_lambdas = 1, lambda_to_forall = 1,unroll_only_formulas = 1, sine = Auto) 0.29/0.89 % No SInE strategy applied 0.29/0.89 % Search class: HGHSM-SMLM31-MHSFFMBN 0.29/0.89 % partial match(1): HGHSM-SMLM31-MHSFFSBN 0.29/0.89 % Scheduled 5 strats onto 2 cores with 360 seconds (360 total) 0.29/0.89 % Starting SubtermCWHack with 37s (1) cores 0.29/0.89 % Starting new_ho_10 with 217s (1) cores 0.29/0.89 % Preprocessing time : 0.052 s 0.29/0.89 % Presaturation interreduction done 0.29/0.89 0.29/0.89 % Proof found! 0.29/0.89 % SZS status Theorem 0.29/0.89 % SZS output start CNFRefutation 0.29/0.89 thf(decl_sort1, type, term: $tType). 0.29/0.89 thf(decl_sort2, type, subst: $tType). 0.29/0.89 thf(decl_sort3, type, d_term: $tType). 0.29/0.89 thf(decl_sort4, type, d_subst: $tType). 0.29/0.89 thf(decl_23, type, one: term). 0.29/0.89 thf(decl_24, type, ap: term > term > term). 0.29/0.89 thf(decl_25, type, lam: term > term). 0.29/0.89 thf(decl_26, type, sub: term > subst > term). 0.29/0.89 thf(decl_27, type, id: subst). 0.29/0.89 thf(decl_28, type, sh: subst). 0.29/0.89 thf(decl_29, type, push: term > subst > subst). 0.29/0.89 thf(decl_30, type, comp: subst > subst > subst). 0.29/0.89 thf(decl_31, type, var: term > $o). 0.29/0.89 thf(decl_32, type, pushprop_lem1v2: $o). 0.29/0.89 thf(decl_33, type, pushprop_lem1_gthm: $o). 0.29/0.89 thf(decl_34, type, axmap: $o). 0.29/0.89 thf(decl_35, type, pushprop_lem0_gthm: $o). 0.29/0.89 thf(decl_36, type, shinj: $o). 0.29/0.89 thf(decl_37, type, hoasinduction_lem1v2: $o). 0.29/0.89 thf(decl_38, type, hoasinduction_lem1v2_gthm: $o). 0.29/0.89 thf(decl_39, type, hoasap: subst > term > subst > term > term). 0.29/0.89 thf(decl_40, type, induction2lem: $o). 0.29/0.89 thf(decl_41, type, hoasinduction_lem3v2_f: $o). 0.29/0.89 thf(decl_42, type, axvarshift: $o). 0.29/0.89 thf(decl_43, type, hoasapinj2: $o). 0.29/0.89 thf(decl_44, type, hoasapnotvar_gthm: $o). 0.29/0.89 thf(decl_45, type, hoasapinj1: $o). 0.29/0.89 thf(decl_46, type, ulamvar1: $o). 0.29/0.89 thf(decl_47, type, induction2lem_lthm: $o). 0.29/0.89 thf(decl_48, type, hoasinduction_lem3v2_gthm: $o). 0.29/0.89 thf(decl_49, type, apnotvar: $o). 0.29/0.89 thf(decl_50, type, pushprop_lthm_orig: $o). 0.29/0.89 thf(decl_51, type, hoasinduction_lem3v2_f_lthm: $o). 0.29/0.89 thf(decl_52, type, hoasinduction_lthm: $o). 0.29/0.89 thf(decl_53, type, hoasinduction_no_psi_cond_lthm: $o). 0.29/0.89 thf(decl_54, type, hoaslaminj: $o). 0.29/0.89 thf(decl_55, type, hoasinduction_lem3aaa: $o). 0.29/0.89 thf(decl_56, type, induction2lem_gthm: $o). 0.29/0.89 thf(decl_57, type, hoasinduction_lem3aa_lthm: $o). 0.29/0.89 thf(decl_58, type, hoasinduction_lem3: $o). 0.29/0.89 thf(decl_59, type, hoasinduction_lem2: $o). 0.29/0.89 thf(decl_60, type, termmset_lthm: $o). 0.29/0.89 thf(decl_61, type, hoasinduction_lem1: $o). 0.29/0.89 thf(decl_62, type, hoaslamnotap_lthm: $o). 0.29/0.89 thf(decl_63, type, pushprop_lem1v2_lthm: $o). 0.29/0.89 thf(decl_64, type, hoasapnotvar: $o). 0.29/0.89 thf(decl_65, type, hoasinduction_lem0: $o). 0.29/0.89 thf(decl_66, type, hoasinduction: $o). 0.29/0.89 thf(decl_67, type, hoasinduction_gthm: $o). 0.29/0.89 thf(decl_68, type, axapp: $o). 0.29/0.89 thf(decl_69, type, hoaslamnotvar_lthm: $o). 0.29/0.89 thf(decl_70, type, pushprop_lem3v2_lthm: $o). 0.29/0.89 thf(decl_71, type, hoasinduction_lem3b_lthm: $o). 0.29/0.89 thf(decl_72, type, ulamvarind: $o). 0.29/0.89 thf(decl_73, type, induction: $o). 0.29/0.89 thf(decl_74, type, hoasinduction_lem3a_lthm: $o). 0.29/0.89 thf(decl_75, type, termmset_gthm: $o). 0.29/0.89 thf(decl_76, type, hoasinduction_lem3aa: $o). 0.29/0.89 thf(decl_77, type, pushprop_lem1v2_gthm: $o). 0.29/0.89 thf(decl_78, type, hoaslamnotap_gthm: $o). 0.29/0.89 thf(decl_79, type, hoaslamnotvar_gthm: $o). 0.29/0.89 thf(decl_80, type, hoasinduction_lem3b_gthm: $o). 0.29/0.89 thf(decl_81, type, pushprop_lem2v2: $o). 0.29/0.89 thf(decl_82, type, hoasinduction_lem3a_gthm: $o). 0.29/0.89 thf(decl_83, type, axclos: $o). 0.29/0.89 thf(decl_84, type, axassoc: $o). 0.29/0.89 thf(decl_85, type, hoasinduction_lem2v2: $o). 0.29/0.89 thf(decl_86, type, pushprop_lthm: $o). 0.29/0.89 thf(decl_87, type, apinj2: $o). 0.29/0.89 thf(decl_88, type, apinj1: $o). 0.29/0.89 thf(decl_89, type, hoasapinj2_lthm: $o). 0.29/0.89 thf(decl_90, type, hoasinduction_lem3v2a: $o). 0.29/0.89 thf(decl_91, type, hoasapinj1_lthm: $o). 0.29/0.89 thf(decl_92, type, hoaslaminj_lthm: $o). 0.29/0.89 thf(decl_93, type, axvarcons: $o). 0.29/0.89 thf(decl_94, type, hoaslam: subst > (subst > term > term) > term). 0.29/0.89 thf(decl_95, type, axscons: $o). 0.29/0.89 thf(decl_96, type, hoasinduction_lem2v2_gthm: $o). 0.29/0.89 thf(decl_97, type, axidr: $o). 0.29/0.89 thf(decl_98, type, pushprop_lem1: $o). 0.29/0.89 thf(decl_99, type, laminj: $o). 0.29/0.89 thf(decl_100, type, hoasinduction_lem3_lthm: $o). 0.29/0.89 thf(decl_101, type, pushprop_lem0: $o). 0.29/0.89 thf(decl_102, type, pushprop_gthm: $o). 0.29/0.89 thf(decl_103, type, axabs: $o). 0.29/0.89 thf(decl_104, type, hoasinduction_lem3v2a_lthm: $o). 0.29/0.89 thf(decl_105, type, hoasinduction_lem2_lthm: $o). 0.29/0.89 thf(decl_106, type, hoasapinj2_gthm: $o). 0.29/0.89 thf(decl_107, type, hoasinduction_p_and_p_prime: (subst > term > subst > $o) > (term > $o) > $o). 0.29/0.89 thf(decl_108, type, hoasinduction_lem1_lthm: $o). 0.29/0.89 thf(decl_109, type, lamnotap: $o). 0.29/0.89 thf(decl_110, type, hoasapinj1_gthm: $o). 0.29/0.89 thf(decl_111, type, hoaslamnotvar: $o). 0.29/0.89 thf(decl_112, type, axidl: $o). 0.29/0.89 thf(decl_113, type, hoaslaminj_gthm: $o). 0.29/0.89 thf(decl_114, type, induction2_lthm: $o). 0.29/0.89 thf(decl_115, type, hoasinduction_lem0_lthm: $o). 0.29/0.89 thf(decl_116, type, substmonoid_lthm: $o). 0.29/0.89 thf(decl_117, type, pushprop: $o). 0.29/0.89 thf(decl_118, type, hoasinduction_lem3_gthm: $o). 0.29/0.89 thf(decl_119, type, hoasinduction_lem2_gthm: $o). 0.29/0.89 thf(decl_120, type, hoasinduction_lem3b: $o). 0.29/0.89 thf(decl_121, type, substmonoid: $o). 0.29/0.89 thf(decl_122, type, lamnotvar: $o). 0.29/0.89 thf(decl_123, type, hoasinduction_lem3a: $o). 0.29/0.89 thf(decl_124, type, hoasinduction_lem1_gthm: $o). 0.29/0.89 thf(decl_125, type, hoasinduction_no_psi_cond: $o). 0.29/0.89 thf(decl_126, type, induction2_gthm: $o). 0.29/0.89 thf(decl_127, type, pushprop_lem2v2_lthm: $o). 0.29/0.89 thf(decl_128, type, hoasvar: subst > term > subst > $o). 0.29/0.89 thf(decl_129, type, hoaslamnotap: $o). 0.29/0.89 thf(decl_130, type, substmonoid_gthm: $o). 0.29/0.89 thf(decl_131, type, ulamvarsh: $o). 0.29/0.89 thf(decl_132, type, induction2: $o). 0.29/0.89 thf(decl_133, type, pushprop_lem3v2: $o). 0.29/0.89 thf(decl_134, type, pushprop_lem2v2_gthm: $o). 0.29/0.89 thf(decl_135, type, pushprop_lem1_lthm: $o). 0.29/0.89 thf(decl_136, type, hoasinduction_lem3v2: $o). 0.29/0.89 thf(decl_137, type, axshiftcons: $o). 0.29/0.89 thf(decl_138, type, termmset: $o). 0.29/0.89 thf(decl_139, type, pushprop_lem0_lthm: $o). 0.29/0.89 thf(decl_140, type, hoasapnotvar_lthm: $o). 0.29/0.89 thf(decl_141, type, hoasinduction_lem3v2_lthm: $o). 0.29/0.89 thf(decl_142, type, pushprop_p_and_p_prime: term > subst > (term > $o) > (term > $o) > $o). 0.29/0.89 thf(decl_143, type, axvarid: $o). 0.29/0.89 thf(decl_144, type, hoasinduction_lthm_3: $o). 0.29/0.89 thf(decl_145, type, d2term: d_term > term). 0.29/0.89 thf(decl_146, type, d2subst: d_subst > subst). 0.29/0.89 thf(decl_147, type, d_one: d_term). 0.29/0.89 thf(decl_148, type, d_id: d_subst). 0.29/0.89 thf(decl_149, type, epred1_0: $o). 0.29/0.89 thf(decl_150, type, epred2_0: $o). 0.29/0.89 thf(decl_151, type, epred3_0: $o). 0.29/0.89 thf(decl_153, type, epred5_0: $o). 0.29/0.89 thf(decl_154, type, epred6_0: $o). 0.29/0.89 thf(decl_155, type, epred7_0: $o). 0.29/0.89 thf(decl_156, type, epred8_2: (subst > term > subst > $o) > term > $o). 0.29/0.89 thf(decl_157, type, epred9_0: $o). 0.29/0.89 thf(decl_160, type, epred12_0: $o). 0.29/0.89 thf(decl_161, type, epred13_0: term > $o). 0.29/0.89 thf(decl_162, type, esk1_0: term). 0.29/0.89 thf(decl_163, type, esk2_0: subst). 0.29/0.89 thf(decl_164, type, epred14_3: (term > $o) > term > subst > term > $o). 0.29/0.89 thf(decl_165, type, esk3_1: subst > d_subst). 0.29/0.89 thf(decl_166, type, esk4_4: term > subst > (term > $o) > (term > $o) > term). 0.29/0.89 thf(decl_167, type, epred15_0: term > $o). 0.29/0.89 thf(decl_168, type, epred16_0: term > $o). 0.29/0.89 thf(decl_169, type, esk5_0: term). 0.29/0.89 thf(decl_170, type, esk6_0: subst). 0.29/0.89 thf(decl_171, type, esk7_4: (term > $o) > (term > $o) > term > subst > term). 0.29/0.89 thf(decl_172, type, esk8_0: term). 0.29/0.89 thf(decl_173, type, esk9_0: term). 0.29/0.89 thf(decl_174, type, esk10_1: term > subst > term > term). 0.29/0.89 thf(decl_175, type, esk11_0: term). 0.29/0.89 thf(decl_176, type, esk12_1: (subst > term > term) > term). 0.29/0.89 thf(decl_177, type, esk13_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_178, type, esk14_0: term). 0.29/0.89 thf(decl_179, type, esk15_0: term). 0.29/0.89 thf(decl_180, type, esk16_0: term). 0.29/0.89 thf(decl_181, type, esk17_0: term). 0.29/0.89 thf(decl_182, type, esk18_0: term). 0.29/0.89 thf(decl_183, type, esk19_0: subst). 0.29/0.89 thf(decl_184, type, esk20_0: term). 0.29/0.89 thf(decl_185, type, esk21_0: subst). 0.29/0.89 thf(decl_186, type, esk22_0: subst). 0.29/0.89 thf(decl_187, type, epred17_0: subst > term > subst > $o). 0.29/0.89 thf(decl_188, type, esk23_0: term). 0.29/0.89 thf(decl_189, type, esk24_2: (subst > term > term) > term > subst). 0.29/0.89 thf(decl_190, type, esk25_2: (subst > term > term) > term > term). 0.29/0.89 thf(decl_191, type, esk26_2: (subst > term > term) > term > subst). 0.29/0.89 thf(decl_192, type, esk27_2: (subst > term > term) > term > subst). 0.29/0.89 thf(decl_193, type, esk28_2: (subst > term > term) > term > term). 0.29/0.89 thf(decl_194, type, esk29_2: (subst > term > term) > term > subst). 0.29/0.89 thf(decl_195, type, esk30_2: (subst > term > term) > term > term). 0.29/0.89 thf(decl_196, type, esk31_2: (subst > term > subst > $o) > term > term). 0.29/0.89 thf(decl_197, type, esk32_1: (subst > term > subst > $o) > subst > term > term). 0.29/0.89 thf(decl_198, type, esk33_1: (subst > term > subst > $o) > term). 0.29/0.89 thf(decl_199, type, epred18_0: subst > term > subst > $o). 0.29/0.89 thf(decl_200, type, esk34_0: term). 0.29/0.89 thf(decl_201, type, esk35_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_202, type, esk36_1: (subst > term > term) > term). 0.29/0.89 thf(decl_203, type, esk37_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_204, type, esk38_1: (subst > term > term) > term). 0.29/0.89 thf(decl_205, type, esk39_2: (subst > term > subst > $o) > term > subst > term > term). 0.29/0.89 thf(decl_206, type, esk40_2: (subst > term > subst > $o) > term > term). 0.29/0.89 thf(decl_207, type, esk41_2: (subst > term > subst > $o) > term > subst). 0.29/0.89 thf(decl_208, type, esk42_2: (subst > term > subst > $o) > term > term). 0.29/0.89 thf(decl_209, type, esk43_2: (subst > term > subst > $o) > term > subst). 0.29/0.89 thf(decl_210, type, esk44_2: (subst > term > subst > $o) > term > subst). 0.29/0.89 thf(decl_211, type, esk45_2: (subst > term > subst > $o) > term > subst). 0.29/0.89 thf(decl_212, type, esk46_2: (subst > term > subst > $o) > term > term). 0.29/0.89 thf(decl_213, type, esk47_2: (subst > term > subst > $o) > term > subst). 0.29/0.89 thf(decl_214, type, esk48_2: (subst > term > subst > $o) > term > subst). 0.29/0.89 thf(decl_215, type, esk49_2: (subst > term > subst > $o) > term > term). 0.29/0.89 thf(decl_216, type, esk50_1: (subst > term > subst > $o) > subst > term > term). 0.29/0.89 thf(decl_217, type, epred19_0: subst > term > subst > $o). 0.29/0.89 thf(decl_218, type, esk51_0: term). 0.29/0.89 thf(decl_219, type, esk52_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_220, type, esk53_1: (subst > term > term) > term). 0.29/0.89 thf(decl_221, type, esk54_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_222, type, esk55_1: (subst > term > term) > term). 0.29/0.89 thf(decl_223, type, epred20_0: term > $o). 0.29/0.89 thf(decl_224, type, epred21_0: term > $o). 0.29/0.89 thf(decl_225, type, esk56_0: term). 0.29/0.89 thf(decl_226, type, esk57_0: subst). 0.29/0.89 thf(decl_227, type, esk58_0: term). 0.29/0.89 thf(decl_228, type, esk59_0: subst). 0.29/0.89 thf(decl_229, type, esk60_4: (term > $o) > (term > $o) > term > subst > term). 0.29/0.89 thf(decl_230, type, epred22_0: subst > term > subst > $o). 0.29/0.89 thf(decl_231, type, epred23_0: term > $o). 0.29/0.89 thf(decl_232, type, esk61_0: term). 0.29/0.89 thf(decl_233, type, esk62_0: term). 0.29/0.89 thf(decl_234, type, esk63_4: (subst > term > subst > $o) > (term > $o) > term > term > subst). 0.29/0.89 thf(decl_235, type, esk64_4: (subst > term > subst > $o) > (term > $o) > term > term > term). 0.29/0.89 thf(decl_236, type, esk65_4: (subst > term > subst > $o) > (term > $o) > term > term > subst). 0.29/0.89 thf(decl_237, type, esk66_4: (subst > term > subst > $o) > (term > $o) > term > term > subst). 0.29/0.89 thf(decl_238, type, esk67_4: (subst > term > subst > $o) > (term > $o) > term > term > subst). 0.29/0.89 thf(decl_239, type, esk68_4: (subst > term > subst > $o) > (term > $o) > term > term > term). 0.29/0.89 thf(decl_240, type, esk69_4: (subst > term > subst > $o) > (term > $o) > term > term > subst). 0.29/0.89 thf(decl_241, type, esk70_4: (subst > term > subst > $o) > (term > $o) > term > term > subst). 0.29/0.89 thf(decl_242, type, esk71_4: (subst > term > subst > $o) > (term > $o) > term > term > term). 0.29/0.89 thf(decl_243, type, esk72_1: (subst > term > subst > $o) > term). 0.29/0.89 thf(decl_244, type, esk73_1: (subst > term > subst > $o) > term). 0.29/0.89 thf(decl_245, type, esk74_0: term). 0.29/0.89 thf(decl_246, type, esk75_0: term). 0.29/0.89 thf(decl_247, type, esk76_0: term). 0.29/0.89 thf(decl_248, type, esk77_0: term). 0.29/0.89 thf(decl_249, type, epred24_0: subst > term > subst > $o). 0.29/0.89 thf(decl_250, type, epred25_0: term > $o). 0.29/0.89 thf(decl_251, type, esk78_0: term). 0.29/0.89 thf(decl_252, type, esk79_1: (subst > term > term) > term). 0.29/0.89 thf(decl_253, type, esk80_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_254, type, esk81_1: (subst > term > term) > term). 0.29/0.89 thf(decl_255, type, esk82_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_256, type, esk83_3: (subst > term > subst > $o) > (term > $o) > term > subst > term > term). 0.29/0.89 thf(decl_257, type, esk84_3: (subst > term > subst > $o) > (term > $o) > term > term). 0.29/0.89 thf(decl_258, type, esk85_3: (subst > term > subst > $o) > (term > $o) > term > term). 0.29/0.89 thf(decl_259, type, esk86_0: term). 0.29/0.89 thf(decl_260, type, esk87_0: term). 0.29/0.89 thf(decl_261, type, esk88_0: term). 0.29/0.89 thf(decl_262, type, esk89_0: term). 0.29/0.89 thf(decl_263, type, esk90_0: term). 0.29/0.89 thf(decl_264, type, esk91_0: term). 0.29/0.89 thf(decl_265, type, esk92_0: term). 0.29/0.89 thf(decl_266, type, esk93_0: term). 0.29/0.89 thf(decl_267, type, esk94_0: term). 0.29/0.89 thf(decl_268, type, esk95_0: term). 0.29/0.89 thf(decl_269, type, esk96_0: subst). 0.29/0.89 thf(decl_270, type, esk97_0: subst). 0.29/0.89 thf(decl_271, type, esk98_0: subst). 0.29/0.89 thf(decl_272, type, epred26_0: term > $o). 0.29/0.89 thf(decl_273, type, epred27_0: term > $o). 0.29/0.89 thf(decl_274, type, esk99_0: term). 0.29/0.89 thf(decl_275, type, esk100_0: subst). 0.29/0.89 thf(decl_276, type, esk101_0: term). 0.29/0.89 thf(decl_277, type, esk102_0: term). 0.29/0.89 thf(decl_278, type, epred28_0: term > $o). 0.29/0.89 thf(decl_279, type, esk103_0: term). 0.29/0.89 thf(decl_280, type, esk104_0: subst). 0.29/0.89 thf(decl_281, type, esk105_1: (term > $o) > term). 0.29/0.89 thf(decl_282, type, epred29_3: (term > $o) > term > subst > term > $o). 0.29/0.89 thf(decl_283, type, esk106_0: term). 0.29/0.89 thf(decl_284, type, esk107_1: (subst > term > term) > term). 0.29/0.89 thf(decl_285, type, esk108_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_286, type, esk109_0: term). 0.29/0.89 thf(decl_287, type, esk110_3: (subst > term > subst > $o) > (term > $o) > term > subst > term > term). 0.29/0.89 thf(decl_288, type, esk111_3: (subst > term > subst > $o) > (term > $o) > term > term). 0.29/0.89 thf(decl_289, type, esk112_2: (subst > term > subst > $o) > (term > $o) > term). 0.29/0.89 thf(decl_290, type, esk113_1: term > subst > term > term). 0.29/0.89 thf(decl_291, type, epred30_0: subst > term > subst > $o). 0.29/0.89 thf(decl_292, type, epred31_0: term > $o). 0.29/0.89 thf(decl_293, type, esk114_0: term). 0.29/0.89 thf(decl_294, type, esk115_1: (subst > term > term) > term). 0.29/0.89 thf(decl_295, type, esk116_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_296, type, esk117_1: (subst > term > term) > term). 0.29/0.89 thf(decl_297, type, esk118_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_298, type, esk119_0: subst). 0.29/0.89 thf(decl_299, type, epred32_1: (subst > term > subst > $o) > term > $o). 0.29/0.89 thf(decl_300, type, epred33_0: subst > term > subst > $o). 0.29/0.89 thf(decl_301, type, esk120_1: (term > $o) > term). 0.29/0.89 thf(decl_302, type, esk121_0: subst). 0.29/0.89 thf(decl_303, type, esk122_0: subst). 0.29/0.89 thf(decl_304, type, esk123_0: subst). 0.29/0.89 thf(decl_305, type, esk124_0: subst). 0.29/0.89 thf(decl_306, type, epred34_0: subst > term > subst > $o). 0.29/0.89 thf(decl_307, type, esk125_0: term). 0.29/0.89 thf(decl_308, type, esk126_1: (subst > term > term) > term). 0.29/0.89 thf(decl_309, type, esk127_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_310, type, esk128_1: (subst > term > term) > term). 0.29/0.89 thf(decl_311, type, esk129_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_312, type, esk130_1: (subst > term > subst > $o) > term). 0.29/0.89 thf(decl_313, type, esk131_1: (subst > term > subst > $o) > term). 0.29/0.89 thf(decl_314, type, esk132_1: (subst > term > subst > $o) > subst > term > term). 0.29/0.89 thf(decl_315, type, esk133_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_316, type, esk134_1: (subst > term > term) > term). 0.29/0.89 thf(decl_317, type, esk135_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_318, type, esk136_0: subst > term > term). 0.29/0.89 thf(decl_319, type, esk137_0: term). 0.29/0.89 thf(decl_320, type, esk138_0: term). 0.29/0.89 thf(decl_321, type, epred35_0: term > $o). 0.29/0.89 thf(decl_322, type, esk139_0: term). 0.29/0.89 thf(decl_323, type, esk140_1: term > term). 0.29/0.89 thf(decl_324, type, esk141_1: (term > $o) > term). 0.29/0.89 thf(decl_325, type, esk142_1: (term > $o) > term). 0.29/0.89 thf(decl_326, type, esk143_1: (term > $o) > term). 0.29/0.89 thf(decl_327, type, esk144_1: (term > $o) > term). 0.29/0.89 thf(decl_328, type, esk145_0: term). 0.29/0.89 thf(decl_329, type, esk146_0: subst). 0.29/0.89 thf(decl_330, type, esk147_0: term). 0.29/0.89 thf(decl_331, type, esk148_0: subst). 0.29/0.89 thf(decl_332, type, epred36_0: term > $o). 0.29/0.89 thf(decl_333, type, epred37_0: term > $o). 0.29/0.89 thf(decl_334, type, esk149_0: term). 0.29/0.89 thf(decl_335, type, esk150_0: subst). 0.29/0.89 thf(decl_336, type, esk151_0: term). 0.29/0.89 thf(decl_337, type, esk152_0: term). 0.29/0.89 thf(decl_338, type, esk153_0: subst). 0.29/0.89 thf(decl_339, type, epred38_0: term > $o). 0.29/0.89 thf(decl_340, type, esk154_0: term). 0.29/0.89 thf(decl_341, type, esk155_0: subst). 0.29/0.89 thf(decl_342, type, esk156_1: (term > $o) > term). 0.29/0.89 thf(decl_343, type, epred39_3: (term > $o) > term > subst > term > $o). 0.29/0.89 thf(decl_344, type, esk157_0: term). 0.29/0.89 thf(decl_345, type, epred40_0: subst > term > subst > $o). 0.29/0.89 thf(decl_346, type, esk158_1: (term > $o) > term). 0.29/0.89 thf(decl_347, type, epred41_1: (subst > term > subst > $o) > term > $o). 0.29/0.89 thf(decl_348, type, esk159_0: term). 0.29/0.89 thf(decl_349, type, esk160_0: term). 0.29/0.89 thf(decl_350, type, esk161_2: (subst > term > subst > $o) > term > subst > term > term). 0.29/0.89 thf(decl_351, type, esk162_2: (subst > term > subst > $o) > term > term). 0.29/0.89 thf(decl_352, type, epred42_0: subst > term > subst > $o). 0.29/0.89 thf(decl_353, type, esk163_0: term). 0.29/0.89 thf(decl_354, type, esk164_1: (subst > term > term) > term). 0.29/0.89 thf(decl_355, type, esk165_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_356, type, esk166_1: (subst > term > term) > term). 0.29/0.89 thf(decl_357, type, esk167_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_358, type, esk168_0: subst). 0.29/0.89 thf(decl_359, type, esk169_0: subst). 0.29/0.89 thf(decl_360, type, esk170_1: term > subst > term > term). 0.29/0.89 thf(decl_361, type, esk171_0: term). 0.29/0.89 thf(decl_362, type, esk172_0: term). 0.29/0.89 thf(decl_363, type, esk173_0: term). 0.29/0.89 thf(decl_364, type, esk174_0: term). 0.29/0.89 thf(decl_365, type, esk175_0: subst > term > term). 0.29/0.89 thf(decl_366, type, esk176_0: subst > term > term). 0.29/0.89 thf(decl_367, type, esk177_0: subst). 0.29/0.89 thf(decl_368, type, esk178_0: term). 0.29/0.89 thf(decl_369, type, esk179_0: term). 0.29/0.89 thf(decl_370, type, esk180_0: subst). 0.29/0.89 thf(decl_371, type, esk181_0: term). 0.29/0.89 thf(decl_372, type, esk182_0: subst). 0.29/0.89 thf(decl_373, type, esk183_0: term). 0.29/0.89 thf(decl_374, type, esk184_0: term). 0.29/0.89 thf(decl_375, type, esk185_2: (subst > term > term) > (subst > term > term) > subst). 0.29/0.89 thf(decl_376, type, esk186_2: (subst > term > term) > (subst > term > term) > term). 0.29/0.89 thf(decl_377, type, esk187_2: (subst > term > term) > (subst > term > term) > subst). 0.29/0.89 thf(decl_378, type, esk188_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_379, type, esk189_1: (subst > term > term) > term). 0.29/0.89 thf(decl_380, type, esk190_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_381, type, esk191_0: term). 0.29/0.89 thf(decl_382, type, esk192_0: term). 0.29/0.89 thf(decl_383, type, esk193_0: term). 0.29/0.89 thf(decl_384, type, esk194_0: term). 0.29/0.89 thf(decl_385, type, esk195_0: term). 0.29/0.89 thf(decl_386, type, esk196_0: term). 0.29/0.89 thf(decl_387, type, esk197_0: term). 0.29/0.89 thf(decl_388, type, esk198_0: term). 0.29/0.89 thf(decl_389, type, esk199_0: term). 0.29/0.89 thf(decl_390, type, esk200_0: term). 0.29/0.89 thf(decl_391, type, esk201_0: term). 0.29/0.89 thf(decl_392, type, esk202_0: term). 0.29/0.89 thf(decl_393, type, epred43_0: subst > term > subst > $o). 0.29/0.89 thf(decl_394, type, esk203_0: term). 0.29/0.89 thf(decl_395, type, esk204_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_396, type, esk205_1: (subst > term > term) > term). 0.29/0.89 thf(decl_397, type, esk206_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_398, type, esk207_1: (subst > term > term) > term). 0.29/0.89 thf(decl_399, type, esk208_2: (subst > term > subst > $o) > term > term). 0.29/0.89 thf(decl_400, type, esk209_1: (subst > term > subst > $o) > subst > term > term). 0.29/0.89 thf(decl_401, type, esk210_0: term). 0.29/0.89 thf(decl_402, type, epred44_0: subst > term > subst > $o). 0.29/0.89 thf(decl_403, type, esk211_0: term). 0.29/0.89 thf(decl_404, type, esk212_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_405, type, esk213_1: (subst > term > term) > term). 0.29/0.89 thf(decl_406, type, esk214_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_407, type, esk215_1: (subst > term > term) > term). 0.29/0.89 thf(decl_408, type, esk216_2: (subst > term > subst > $o) > term > term). 0.29/0.89 thf(decl_409, type, esk217_1: (subst > term > subst > $o) > subst > term > term). 0.29/0.89 thf(decl_410, type, esk218_2: (subst > term > subst > $o) > term > term). 0.29/0.89 thf(decl_411, type, esk219_1: (subst > term > subst > $o) > subst > term > term). 0.29/0.89 thf(decl_412, type, epred45_0: subst > term > subst > $o). 0.29/0.89 thf(decl_413, type, esk220_0: term). 0.29/0.89 thf(decl_414, type, esk221_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_415, type, esk222_1: (subst > term > term) > term). 0.29/0.89 thf(decl_416, type, esk223_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_417, type, esk224_1: (subst > term > term) > term). 0.29/0.89 thf(decl_418, type, epred46_0: term > $o). 0.29/0.89 thf(decl_419, type, esk225_0: term). 0.29/0.89 thf(decl_420, type, esk226_1: (term > $o) > term). 0.29/0.89 thf(decl_421, type, esk227_1: (term > $o) > term). 0.29/0.89 thf(decl_422, type, esk228_1: (term > $o) > term). 0.29/0.89 thf(decl_423, type, esk229_1: (term > $o) > term). 0.29/0.89 thf(decl_424, type, esk230_0: term). 0.29/0.89 thf(decl_425, type, esk231_1: term > subst > term > term). 0.29/0.89 thf(decl_426, type, esk232_1: (subst > term > subst > $o) > subst). 0.29/0.89 thf(decl_427, type, esk233_1: (subst > term > subst > $o) > term). 0.29/0.89 thf(decl_428, type, esk234_1: (subst > term > subst > $o) > subst). 0.29/0.89 thf(decl_429, type, esk235_1: (subst > term > subst > $o) > subst). 0.29/0.89 thf(decl_430, type, epred47_0: subst > term > subst > $o). 0.29/0.89 thf(decl_431, type, esk236_0: term). 0.29/0.89 thf(decl_432, type, epred48_0: subst > term > subst > $o). 0.29/0.89 thf(decl_433, type, esk237_1: (term > $o) > term). 0.29/0.89 thf(decl_434, type, epred49_1: (subst > term > subst > $o) > term > $o). 0.29/0.89 thf(decl_435, type, epred50_0: subst > term > subst > $o). 0.29/0.89 thf(decl_436, type, esk238_0: term). 0.29/0.89 thf(decl_437, type, esk239_0: term). 0.29/0.89 thf(decl_438, type, esk240_3: (subst > term > subst > $o) > term > term > subst). 0.29/0.89 thf(decl_439, type, esk241_3: (subst > term > subst > $o) > term > term > term). 0.29/0.89 thf(decl_440, type, esk242_3: (subst > term > subst > $o) > term > term > subst). 0.29/0.89 thf(decl_441, type, esk243_3: (subst > term > subst > $o) > term > term > subst). 0.29/0.89 thf(decl_442, type, esk244_1: (subst > term > subst > $o) > term). 0.29/0.89 thf(decl_443, type, esk245_1: (subst > term > subst > $o) > term). 0.29/0.89 thf(decl_444, type, esk246_1: (subst > term > subst > $o) > subst). 0.29/0.89 thf(decl_445, type, esk247_1: (subst > term > subst > $o) > term). 0.29/0.89 thf(decl_446, type, esk248_1: (subst > term > subst > $o) > subst). 0.29/0.89 thf(decl_447, type, esk249_1: (subst > term > subst > $o) > subst). 0.29/0.89 thf(decl_448, type, esk250_2: (subst > term > term) > (subst > term > term) > subst). 0.29/0.89 thf(decl_449, type, esk251_2: (subst > term > term) > (subst > term > term) > term). 0.29/0.89 thf(decl_450, type, esk252_2: (subst > term > term) > (subst > term > term) > subst). 0.29/0.89 thf(decl_451, type, esk253_2: (subst > term > term) > (subst > term > term) > subst). 0.29/0.89 thf(decl_452, type, esk254_2: (subst > term > term) > (subst > term > term) > term). 0.29/0.89 thf(decl_453, type, esk255_2: (subst > term > term) > (subst > term > term) > subst). 0.29/0.89 thf(decl_454, type, esk256_0: subst > term > term). 0.29/0.89 thf(decl_455, type, esk257_0: subst > term > term). 0.29/0.89 thf(decl_456, type, esk258_0: subst). 0.29/0.89 thf(decl_457, type, esk259_0: term). 0.29/0.89 thf(decl_458, type, epred51_0: subst > term > subst > $o). 0.29/0.89 thf(decl_459, type, esk260_1: (term > $o) > term). 0.29/0.89 thf(decl_460, type, epred52_0: term > $o). 0.29/0.89 thf(decl_461, type, esk261_0: term). 0.29/0.89 thf(decl_462, type, esk262_1: term > term). 0.29/0.89 thf(decl_463, type, esk263_0: term). 0.29/0.89 thf(decl_464, type, epred53_1: (subst > term > subst > $o) > term > $o). 0.29/0.89 thf(decl_465, type, esk264_1: (term > $o) > term). 0.29/0.89 thf(decl_466, type, esk265_1: (term > $o) > term). 0.29/0.89 thf(decl_467, type, esk266_1: (term > $o) > term). 0.29/0.89 thf(decl_468, type, esk267_1: (term > $o) > term). 0.29/0.89 thf(decl_469, type, esk268_0: term). 0.29/0.89 thf(decl_470, type, esk269_1: (subst > term > term) > term). 0.29/0.89 thf(decl_471, type, esk270_1: (subst > term > term) > subst). 0.29/0.89 thf(decl_472, type, esk271_1: term > subst > term > term). 0.29/0.89 thf(decl_473, type, esk272_0: term). 0.29/0.89 thf(decl_474, type, esk273_0: term). 0.29/0.89 thf(decl_475, type, esk274_0: term). 0.29/0.89 thf(decl_476, type, esk275_0: term). 0.29/0.89 thf(decl_477, type, esk276_3: (term > $o) > term > subst > term). 0.29/0.89 thf(decl_478, type, esk277_3: (term > $o) > term > subst > term). 0.29/0.89 thf(decl_479, type, esk278_3: (term > $o) > term > subst > term). 0.29/0.89 thf(decl_480, type, esk279_3: (term > $o) > term > subst > term). 0.29/0.89 thf(decl_481, type, epred54_0: term > $o). 0.29/0.89 thf(decl_482, type, esk280_0: term). 0.29/0.89 thf(decl_483, type, esk281_0: subst). 0.29/0.89 thf(decl_484, type, esk282_1: term > term). 0.29/0.89 thf(decl_485, type, esk283_2: (subst > term > subst > $o) > (term > $o) > term). 0.29/0.89 thf(decl_486, type, esk284_1: term > d_term). 0.29/0.89 thf(alg444_1, axiom, (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((![X5:subst]:(?[X6:d_subst]:(((X5)=(d2subst @ X6))))&((one)=(d2term @ d_one)))&((ap @ (d2term @ d_one) @ (d2term @ d_one))=(d2term @ d_one)))&((lam @ (d2term @ d_one))=(d2term @ d_one)))&((push @ (d2term @ d_one) @ (d2subst @ d_id))=(d2subst @ d_id)))&((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))=(d2term @ d_one)))&((pushprop_p_and_p_prime)=(^[X2:term, X3:subst, X1:term > $o, X4:term > $o]:(![X7:term]:((((X4 @ X7))<=>((X1 @ (sub @ X7 @ (push @ X2 @ X3))))))))))&(![X1:term > $o, X4:term > $o, X2:term, X3:subst]:((~(![X7:term]:(((X4 @ X7)<=>(X1 @ (sub @ X7 @ (push @ X2 @ X3))))))|(X4 @ one)|~((X1 @ X2))))<=>(pushprop_lem1v2)))&(pushprop_lem0_gthm))&(![X2:term, X8:term]:((((X2)=(X8))|((sub @ X2 @ sh)!=(sub @ X8 @ sh))))<=>(shinj)))&(hoasinduction_lem1v2_gthm))&((hoasinduction_lem3v2_f)<=>![X8:term]:(~(![X9:subst > term > term]:(~(![X2:term, X3:subst]:(((sub @ X8 @ (push @ X2 @ X3))=(X9 @ X3 @ X2)))))))))&(axvarshift))&(![X2:term, X8:term, X10:term, X11:term]:((((ap @ (sub @ X2 @ id) @ X10)!=(ap @ (sub @ X8 @ id) @ X11))|((X10)=(X11))))<=>(hoasapinj2)))&~((ulamvar1)))&(((((![X1:term > $o, X12:term]:((~(![X2:term]:(((X1 @ (lam @ X2))|~((X1 @ X2)))))|(X1 @ X12)|~(![X2:term, X8:term]:((~((X1 @ X2))|~((X1 @ X8))|(X1 @ (ap @ X2 @ X8)))))|~(![X2:term]:(((X1 @ X2)|~((var @ X2)))))))=>![X1:term > $o, X13:term, X14:subst]:((~(![X2:term]:((~(![X8:term]:(((X1 @ (sub @ X2 @ (push @ X8 @ id)))|~((X1 @ X8)))))|(X1 @ (lam @ X2)))))|(X1 @ (sub @ X13 @ X14))|~(![X8:term]:((~((var @ X8))|(X1 @ (sub @ X8 @ X14)))))|~(![X2:term, X8:term]:(((X1 @ (ap @ X2 @ X8))|~((X1 @ X8))|~((X1 @ X2))))))))<=![X3:subst]:(((X3)=(comp @ X3 @ id))))<=![X2:term, X3:subst]:(((X3)=(comp @ sh @ (push @ X2 @ X3)))))<=![X2:term, X3:subst]:(((X2)=(sub @ one @ (push @ X2 @ X3)))))<=>(induction2lem_lthm)))&(hoasinduction_lem3v2_gthm))&(apnotvar))&(![X15:subst > term > subst > $o, X16:term]:(((X15 @ id @ (lam @ (sub @ X16 @ (push @ one @ sh))) @ id)|~(![X8:term]:((~((X15 @ id @ X8 @ id))|(X15 @ id @ (sub @ X16 @ (push @ X8 @ id)) @ id))))|~(![X9:subst > term > term, X17:term]:(((X15 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X18:subst, X19:term, X20:subst]:(((X9 @ (comp @ X18 @ X20) @ (sub @ X19 @ X20))=(sub @ X17 @ (push @ (sub @ X19 @ X20) @ (comp @ X18 @ X20))))))|~(![X21:subst, X22:term, X23:subst]:(((sub @ (X9 @ X21 @ X22) @ X23)=(sub @ (sub @ X17 @ (push @ X22 @ X21)) @ X23))))|~(![X2:term]:(((X15 @ id @ (X9 @ id @ X2) @ id)|~((X15 @ id @ X2 @ id))))))))))<=>(hoasinduction_lem3aaa)))&(![X24:subst > term > subst > $o, X25:term]:((~(![X9:subst > term > term]:((~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))|(X24 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X2:term]:(((X24 @ id @ (X9 @ id @ X2) @ id)|~((X24 @ id @ X2 @ id))))))))|(X24 @ id @ (lam @ (sub @ X25 @ (push @ one @ sh))) @ id)|~(![X8:term]:(((X24 @ id @ (sub @ X25 @ (push @ X8 @ id)) @ id)|~((X24 @ id @ X8 @ id)))))))<=>(hoasinduction_lem3aa_lthm)))&((hoasinduction_lem3)<=>![X27:subst > term > subst > $o, X28:term]:((~(![X3:subst, X2:term, X26:subst, X29:subst]:((~((X27 @ X3 @ X2 @ (comp @ X29 @ X26)))|(X27 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26))))|~(![X3:subst, X2:term, X26:subst, X29:subst]:(((X27 @ X3 @ X2 @ (comp @ X29 @ X26))|~((X27 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26)))))|~(![X8:term]:(((X27 @ id @ (sub @ X28 @ (push @ X8 @ id)) @ id)|~((X27 @ id @ X8 @ id)))))|(X27 @ id @ (lam @ X28) @ id)|~(![X9:subst > term > term]:((~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))|~(![X2:term]:((~((X27 @ id @ X2 @ id))|(X27 @ id @ (X9 @ id @ X2) @ id))))|(X27 @ id @ (lam @ (X9 @ sh @ one)) @ id))))))))&((![X2:term]:(((X2)=(sub @ X2 @ id)))=>![X2:term]:(((X2)=(sub @ X2 @ id))))<=>(termmset_lthm)))&((![X1:term > $o, X4:term > $o, X2:term, X3:subst]:((~((X1 @ X2))|~(![X7:term]:(((X4 @ X7)<=>(X1 @ (sub @ X7 @ (push @ X2 @ X3))))))|(X4 @ one)))<=![X2:term, X3:subst]:(((X2)=(sub @ one @ (push @ X2 @ X3)))))<=>(pushprop_lem1v2_lthm)))&(hoasapnotvar))&(pushprop_lem3v2_lthm))&(pushprop_lem1v2_gthm))&(hoaslamnotvar_gthm))&(hoasinduction_lem3a_gthm))&(axclos))&(axassoc))&(![X30:subst > term > subst > $o, X4:term > $o, X31:term, X32:term]:((~(![X3:subst, X2:term, X26:subst, X29:subst]:((~((X30 @ X3 @ X2 @ (comp @ X29 @ X26)))|(X30 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26))))|~(![X3:subst, X2:term, X26:subst, X29:subst]:((~((X30 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26))|(X30 @ X3 @ X2 @ (comp @ X29 @ X26)))))|~(![X7:term]:(((X4 @ X7)<=>(X30 @ id @ X7 @ id))))|~((X4 @ X32))|(X4 @ (ap @ X31 @ X32))|~((X4 @ X31))|~(![X2:term, X8:term]:((~((X30 @ id @ X8 @ id))|(X30 @ id @ (ap @ (sub @ X2 @ id) @ X8) @ id)|~((X30 @ id @ X2 @ id)))))))<=>(hoasinduction_lem2v2)))&(pushprop_lthm))&((apinj1)<=>![X2:term, X8:term, X10:term, X11:term]:((((X2)=(X8))|((ap @ X2 @ X10)!=(ap @ X8 @ X11))))))&(![X33:subst > term > subst > $o, X4:term > $o, X34:term]:((~(![X9:subst > term > term]:(((X33 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X2:term]:(((X33 @ id @ (X9 @ id @ X2) @ id)|~((X33 @ id @ X2 @ id)))))|~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26))))))))|~(![X7:term]:(((X4 @ X7)<=>(X33 @ id @ X7 @ id))))|(X4 @ (lam @ X34))|~(![X8:term]:(((X4 @ (sub @ X34 @ (push @ X8 @ id)))|~((X4 @ X8)))))))<=>(hoasinduction_lem3v2a)))&((hoasapinj1_lthm)<=>(![X2:term]:(((X2)=(sub @ X2 @ id)))=>(![X2:term, X8:term, X10:term, X11:term]:((((ap @ (sub @ X2 @ id) @ X10)!=(ap @ (sub @ X8 @ id) @ X11))|((X2)=(X8))))<=![X2:term, X8:term, X10:term, X11:term]:((((X2)=(X8))|((ap @ X2 @ X10)!=(ap @ X8 @ X11))))))))&((axvarcons)<=>![X2:term, X3:subst]:(((X2)=(sub @ one @ (push @ X2 @ X3))))))&((axscons)<=>![X3:subst]:(((X3)=(push @ (sub @ one @ X3) @ (comp @ sh @ X3))))))&(hoasinduction_lem2v2_gthm))&((axidr)<=>![X3:subst]:(((X3)=(comp @ X3 @ id)))))&(![X1:term > $o, X35:term > $o, X2:term, X3:subst, X8:term]:((~((X1 @ X2))|(X35 @ (sub @ X2 @ (push @ X8 @ X3)))))<=>(pushprop_lem1)))&(((![X36:subst > term > subst > $o, X25:term]:((~(![X9:subst > term > term]:((~(![X2:term]:((~((X36 @ id @ X2 @ id))|(X36 @ id @ (X9 @ id @ X2) @ id))))|(X36 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26))))))))|(X36 @ id @ (lam @ (sub @ X25 @ (push @ one @ sh))) @ id)|~(![X8:term]:(((X36 @ id @ (sub @ X25 @ (push @ X8 @ id)) @ id)|~((X36 @ id @ X8 @ id)))))))=>![X37:subst > term > subst > $o, X28:term]:(((X37 @ id @ (lam @ X28) @ id)|~(![X8:term]:(((X37 @ id @ (sub @ X28 @ (push @ X8 @ id)) @ id)|~((X37 @ id @ X8 @ id)))))|~(![X9:subst > term > term]:((~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))|~(![X2:term]:((~((X37 @ id @ X2 @ id))|(X37 @ id @ (X9 @ id @ X2) @ id))))|(X37 @ id @ (lam @ (X9 @ sh @ one)) @ id))))|~(![X3:subst, X2:term, X26:subst, X29:subst]:((~((X37 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26))|(X37 @ X3 @ X2 @ (comp @ X29 @ X26)))))|~(![X3:subst, X2:term, X26:subst, X29:subst]:((~((X37 @ X3 @ X2 @ (comp @ X29 @ X26)))|(X37 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26)))))))<=![X2:term]:(((X2)=(sub @ X2 @ id))))<=>(hoasinduction_lem3_lthm)))&(![X1:term > $o, X2:term, X3:subst]:(~(![X4:term > $o]:(~(![X7:term]:(((X4 @ X7)<=>(X1 @ (sub @ X7 @ (push @ X2 @ X3)))))))))<=>(pushprop_lem0)))&(pushprop_gthm))&((hoasinduction_lem3v2a_lthm)<=>((![X2:term]:(((X2)=(sub @ X2 @ id)))=>![X38:subst > term > subst > $o, X4:term > $o, X34:term]:((~(![X9:subst > term > term]:(((X38 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X2:term]:(((X38 @ id @ (X9 @ id @ X2) @ id)|~((X38 @ id @ X2 @ id)))))|~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26))))))))|(X4 @ (lam @ X34))|~(![X8:term]:((~((X4 @ X8))|(X4 @ (sub @ X34 @ (push @ X8 @ id))))))|~(![X7:term]:(((X4 @ X7)<=>(X38 @ id @ X7 @ id)))))))<=![X8:term]:(~(![X9:subst > term > term]:(~(![X2:term, X3:subst]:(((sub @ X8 @ (push @ X2 @ X3))=(X9 @ X3 @ X2))))))))))&(hoasinduction_lem2_lthm))&(hoasinduction_lem1_lthm))&~((lamnotap)))&(hoasapinj1_gthm))&((axidl)<=>![X3:subst]:(((X3)=(comp @ id @ X3)))))&((hoasinduction_lem0_lthm)<=>![X39:subst > term > subst > $o]:(~(![X4:term > $o]:(~(![X7:term]:(((X4 @ X7)<=>(X39 @ id @ X7 @ id)))))))))&((substmonoid_lthm)<=>(((![X3:subst]:(((X3)=(comp @ id @ X3)))&![X3:subst]:(((X3)=(comp @ X3 @ id))))<=![X3:subst]:(((X3)=(comp @ X3 @ id))))<=![X3:subst]:(((X3)=(comp @ id @ X3))))))&(hoasinduction_lem3_gthm))&(lamnotvar))&(hoasinduction_lem1_gthm))&(![X40:subst > term > subst > $o, X41:term]:((~(![X2:term, X8:term]:(((X40 @ id @ (ap @ (sub @ X2 @ id) @ X8) @ id)|~((X40 @ id @ X8 @ id))|~((X40 @ id @ X2 @ id)))))|(X40 @ id @ X41 @ id)|~(![X9:subst > term > term]:((~(![X2:term]:((~((X40 @ id @ X2 @ id))|(X40 @ id @ (X9 @ id @ X2) @ id))))|(X40 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26))))))))))<=>(hoasinduction_no_psi_cond)))&(induction2_gthm))&(pushprop_lem2v2_lthm))&((hoaslamnotap)<=>![X9:subst > term > term, X42:term, X43:term]:((~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))|((lam @ (X9 @ sh @ one))!=(ap @ (sub @ X42 @ id) @ X43))))))&(![X1:term > $o, X44:term]:((~(![X2:term]:((~((var @ X2))|(X1 @ X2))))|~(![X2:term]:((~(![X8:term]:(((X1 @ (sub @ X2 @ (push @ X8 @ id)))|~((X1 @ X8)))))|(X1 @ (lam @ X2)))))|(X1 @ X44)|~(![X2:term, X8:term]:((~((X1 @ X2))|(X1 @ (ap @ X2 @ X8))|~((X1 @ X8)))))))<=>(induction2)))&(pushprop_lem3v2))&(pushprop_lem2v2_gthm))&((pushprop_lem1_lthm)<=>((![X1:term > $o, X45:term > $o, X2:term, X3:subst, X8:term]:(((X45 @ (sub @ X2 @ (push @ X8 @ X3)))|~((X1 @ X2))))<=![X2:term, X3:subst]:(((X3)=(comp @ sh @ (push @ X2 @ X3)))))<=![X2:term, X3:subst]:(((X2)=(sub @ one @ (push @ X2 @ X3)))))))&(![X46:subst > term > subst > $o, X4:term > $o, X47:term]:((~(![X9:subst > term > term]:(((X46 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X2:term]:((~((X46 @ id @ X2 @ id))|(X46 @ id @ (X9 @ id @ X2) @ id))))|~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26))))))))|(X4 @ (lam @ X47))|~(![X8:term]:(((X4 @ (sub @ X47 @ (push @ X8 @ id)))|~((X4 @ X8)))))|~(![X7:term]:(((X4 @ X7)<=>(X46 @ id @ X7 @ id))))|~(![X3:subst, X2:term, X26:subst, X29:subst]:((~((X46 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26))|(X46 @ X3 @ X2 @ (comp @ X29 @ X26)))))|~(![X3:subst, X2:term, X26:subst, X29:subst]:((~((X46 @ X3 @ X2 @ (comp @ X29 @ X26)))|(X46 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26))))))<=>(hoasinduction_lem3v2)))&((axshiftcons)<=>![X2:term, X3:subst]:(((X3)=(comp @ sh @ (push @ X2 @ X3))))))&(![X1:term > $o, X2:term, X3:subst]:(~(![X4:term > $o]:(~(![X7:term]:(((X4 @ X7)<=>(X1 @ (sub @ X7 @ (push @ X2 @ X3)))))))))<=>(pushprop_lem0_lthm)))&(hoasapnotvar_lthm))&((axvarid)<=>![X2:term]:(((X2)=(sub @ X2 @ id)))))&((hoasinduction_lthm_3)<=>((![X1:term > $o, X44:term]:((~(![X2:term]:((~(![X8:term]:((~((X1 @ X8))|(X1 @ (sub @ X2 @ (push @ X8 @ id))))))|(X1 @ (lam @ X2)))))|(X1 @ X44)|~(![X2:term, X8:term]:((~((X1 @ X2))|~((X1 @ X8))|(X1 @ (ap @ X2 @ X8)))))|~(![X2:term]:((~((var @ X2))|(X1 @ X2))))))=>((![X48:subst > term > subst > $o, X4:term > $o, X34:term]:((~(![X8:term]:((~((X4 @ X8))|(X4 @ (sub @ X34 @ (push @ X8 @ id))))))|(X4 @ (lam @ X34))|~(![X7:term]:(((X4 @ X7)<=>(X48 @ id @ X7 @ id))))|~(![X9:subst > term > term]:((~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))|(X48 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X2:term]:(((X48 @ id @ (X9 @ id @ X2) @ id)|~((X48 @ id @ X2 @ id))))))))))=>![X49:subst > term > subst > $o, X50:term]:((~(![X2:term, X8:term]:((~((X49 @ id @ X8 @ id))|(X49 @ id @ (ap @ (sub @ X2 @ id) @ X8) @ id)|~((X49 @ id @ X2 @ id)))))|(X49 @ id @ X50 @ id)|~(![X9:subst > term > term]:(((X49 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X2:term]:(((X49 @ id @ (X9 @ id @ X2) @ id)|~((X49 @ id @ X2 @ id)))))|~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26))))))))|~(![X2:term]:(((X49 @ id @ X2 @ id)|~((var @ (sub @ X2 @ id))))))|~(![X3:subst, X2:term, X26:subst, X29:subst]:((~((X49 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26))|(X49 @ X3 @ X2 @ (comp @ X29 @ X26)))))|~(![X3:subst, X2:term, X26:subst, X29:subst]:(((X49 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26)|~((X49 @ X3 @ X2 @ (comp @ X29 @ X26)))))))))<=![X2:term]:(((X2)=(sub @ X2 @ id)))))<=![X51:subst > term > subst > $o]:(~(![X4:term > $o]:(~(![X7:term]:(((X4 @ X7)<=>(X51 @ id @ X7 @ id))))))))))&((hoasinduction_lem3v2_lthm)<=>(![X52:subst > term > subst > $o, X4:term > $o, X47:term]:((~(![X9:subst > term > term]:((~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))|~(![X2:term]:(((X52 @ id @ (X9 @ id @ X2) @ id)|~((X52 @ id @ X2 @ id)))))|(X52 @ id @ (lam @ (X9 @ sh @ one)) @ id))))|~(![X8:term]:((~((X4 @ X8))|(X4 @ (sub @ X47 @ (push @ X8 @ id))))))|(X4 @ (lam @ X47))|~(![X7:term]:(((X4 @ X7)<=>(X52 @ id @ X7 @ id))))|~(![X3:subst, X2:term, X26:subst, X29:subst]:(((X52 @ X3 @ X2 @ (comp @ X29 @ X26))|~((X52 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26)))))|~(![X3:subst, X2:term, X26:subst, X29:subst]:((~((X52 @ X3 @ X2 @ (comp @ X29 @ X26)))|(X52 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26))))))<=![X2:term]:(((X2)=(sub @ X2 @ id))))))&(![X2:term]:(((X2)=(sub @ X2 @ id)))<=>(termmset)))&(ulamvarsh))&(substmonoid_gthm))&~((hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id))))&((hoasinduction_lem3a)<=>![X53:subst > term > subst > $o, X54:term]:((~(![X9:subst > term > term]:((~(![X2:term]:((~((X53 @ id @ X2 @ id))|(X53 @ id @ (X9 @ id @ X2) @ id))))|(X53 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26))))))))|(X53 @ id @ (lam @ X54) @ id)|~(![X8:term]:(((X53 @ id @ (sub @ X54 @ (push @ X8 @ id)) @ id)|~((X53 @ id @ X8 @ id)))))))))&((![X3:subst]:(((X3)=(comp @ X3 @ id)))&![X3:subst]:(((X3)=(comp @ id @ X3))))<=>(substmonoid)))&((hoasinduction_lem3b)<=>![X8:term]:(~(![X9:subst > term > term]:(((X9 @ sh @ one)!=(sub @ X8 @ (push @ one @ sh))))))))&(hoasinduction_lem2_gthm))&(pushprop))&(((![X1:term > $o, X44:term]:((~(![X2:term]:(((X1 @ X2)|~((var @ X2)))))|(X1 @ X44)|~(![X2:term]:((~(![X8:term]:((~((X1 @ X8))|(X1 @ (sub @ X2 @ (push @ X8 @ id))))))|(X1 @ (lam @ X2)))))|~(![X2:term, X8:term]:((~((X1 @ X2))|(X1 @ (ap @ X2 @ X8))|~((X1 @ X8)))))))<=![X1:term > $o, X13:term, X14:subst]:((~(![X2:term, X8:term]:((~((X1 @ X2))|(X1 @ (ap @ X2 @ X8))|~((X1 @ X8)))))|(X1 @ (sub @ X13 @ X14))|~(![X8:term]:(((X1 @ (sub @ X8 @ X14))|~((var @ X8)))))|~(![X2:term]:((~(![X8:term]:(((X1 @ (sub @ X2 @ (push @ X8 @ id)))|~((X1 @ X8)))))|(X1 @ (lam @ X2))))))))<=![X2:term]:(((X2)=(sub @ X2 @ id))))<=>(induction2_lthm)))&(hoaslaminj_gthm))&(hoaslamnotvar))&(hoasapinj2_gthm))&(axabs))&((laminj)<=>![X2:term, X8:term]:((((lam @ X2)!=(lam @ X8))|((X2)=(X8))))))&((![X2:term, X3:subst]:(((X2)=(sub @ one @ (push @ X2 @ X3))))=>(![X2:term, X3:subst]:(((X3)=(comp @ sh @ (push @ X2 @ X3))))=>(![X9:subst > term > term, X55:subst > term > term, X56:subst, X57:term]:((~(![X3:subst, X2:term, X26:subst]:(((sub @ (X55 @ X3 @ X2) @ X26)=(X55 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))|((lam @ (X9 @ sh @ one))!=(lam @ (X55 @ sh @ one)))|((X9 @ X56 @ X57)=(X55 @ X56 @ X57))|~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))))<=![X2:term, X8:term]:((((X2)=(X8))|((lam @ X2)!=(lam @ X8)))))))<=>(hoaslaminj_lthm)))&((hoasapinj2_lthm)<=>(![X2:term, X8:term, X10:term, X11:term]:((((ap @ X2 @ X10)!=(ap @ X8 @ X11))|((X10)=(X11))))=>![X2:term, X8:term, X10:term, X11:term]:((((ap @ (sub @ X2 @ id) @ X10)!=(ap @ (sub @ X8 @ id) @ X11))|((X10)=(X11)))))))&((apinj2)<=>![X2:term, X8:term, X10:term, X11:term]:((((ap @ X2 @ X10)!=(ap @ X8 @ X11))|((X10)=(X11))))))&(pushprop_lem2v2))&(hoasinduction_lem3b_gthm))&(hoaslamnotap_gthm))&(![X58:subst > term > subst > $o, X25:term]:((~(![X8:term]:(((X58 @ id @ (sub @ X25 @ (push @ X8 @ id)) @ id)|~((X58 @ id @ X8 @ id)))))|(X58 @ id @ (lam @ (sub @ X25 @ (push @ one @ sh))) @ id)|~(![X9:subst > term > term]:((~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))|(X58 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X2:term]:(((X58 @ id @ (X9 @ id @ X2) @ id)|~((X58 @ id @ X2 @ id))))))))))<=>(hoasinduction_lem3aa)))&(termmset_gthm))&((hoasinduction_lem3a_lthm)<=>((![X59:subst > term > subst > $o, X25:term]:((~(![X8:term]:((~((X59 @ id @ X8 @ id))|(X59 @ id @ (sub @ X25 @ (push @ X8 @ id)) @ id))))|(X59 @ id @ (lam @ (sub @ X25 @ (push @ one @ sh))) @ id)|~(![X9:subst > term > term]:((~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))|~(![X2:term]:((~((X59 @ id @ X2 @ id))|(X59 @ id @ (X9 @ id @ X2) @ id))))|(X59 @ id @ (lam @ (X9 @ sh @ one)) @ id))))))=>![X60:subst > term > subst > $o, X54:term]:(((X60 @ id @ (lam @ X54) @ id)|~(![X8:term]:((~((X60 @ id @ X8 @ id))|(X60 @ id @ (sub @ X54 @ (push @ X8 @ id)) @ id))))|~(![X9:subst > term > term]:((~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))|(X60 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X2:term]:(((X60 @ id @ (X9 @ id @ X2) @ id)|~((X60 @ id @ X2 @ id)))))))))))<=![X2:term]:(((X2)=(sub @ X2 @ id))))))&(![X1:term > $o, X12:term]:((~(![X2:term, X8:term]:(((X1 @ (ap @ X2 @ X8))|~((X1 @ X8))|~((X1 @ X2)))))|~(![X2:term]:((~((X1 @ X2))|(X1 @ (lam @ X2)))))|(X1 @ X12)|~(![X2:term]:((~((var @ X2))|(X1 @ X2))))))<=>(induction)))&(ulamvarind))&(![X8:term]:(~(![X9:subst > term > term]:(((X9 @ sh @ one)!=(sub @ X8 @ (push @ one @ sh))))))<=>(hoasinduction_lem3b_lthm)))&(hoaslamnotvar_lthm))&(axapp))&(hoasinduction_gthm))&((hoasinduction)<=>![X61:subst > term > subst > $o, X50:term]:((~(![X2:term]:((~((var @ (sub @ X2 @ id)))|(X61 @ id @ X2 @ id))))|(X61 @ id @ X50 @ id)|~(![X9:subst > term > term]:((~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))|(X61 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X2:term]:((~((X61 @ id @ X2 @ id))|(X61 @ id @ (X9 @ id @ X2) @ id)))))))|~(![X2:term, X8:term]:((~((X61 @ id @ X2 @ id))|(X61 @ id @ (ap @ (sub @ X2 @ id) @ X8) @ id)|~((X61 @ id @ X8 @ id)))))|~(![X3:subst, X2:term, X26:subst, X29:subst]:(((X61 @ X3 @ X2 @ (comp @ X29 @ X26))|~((X61 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26)))))|~(![X3:subst, X2:term, X26:subst, X29:subst]:((~((X61 @ X3 @ X2 @ (comp @ X29 @ X26)))|(X61 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26))))))))&(![X62:subst > term > subst > $o]:(~(![X4:term > $o]:(~(![X7:term]:(((X4 @ X7)<=>(X62 @ id @ X7 @ id)))))))<=>(hoasinduction_lem0)))&(hoaslamnotap_lthm))&(hoasinduction_lem1))&(![X63:subst > term > subst > $o, X64:term, X65:term]:((~(![X3:subst, X2:term, X26:subst, X29:subst]:((~((X63 @ X3 @ X2 @ (comp @ X29 @ X26)))|(X63 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26))))|(X63 @ id @ (ap @ X64 @ X65) @ id)|~((X63 @ id @ X65 @ id))|~((X63 @ id @ X64 @ id))|~(![X2:term, X8:term]:((~((X63 @ id @ X2 @ id))|(X63 @ id @ (ap @ (sub @ X2 @ id) @ X8) @ id)|~((X63 @ id @ X8 @ id)))))|~(![X3:subst, X2:term, X26:subst, X29:subst]:(((X63 @ X3 @ X2 @ (comp @ X29 @ X26))|~((X63 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26)))))))<=>(hoasinduction_lem2)))&(induction2lem_gthm))&((hoaslaminj)<=>![X9:subst > term > term, X55:subst > term > term, X56:subst, X57:term]:((~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))|((X9 @ X56 @ X57)=(X55 @ X56 @ X57))|((lam @ (X9 @ sh @ one))!=(lam @ (X55 @ sh @ one)))|~(![X3:subst, X2:term, X26:subst]:(((sub @ (X55 @ X3 @ X2) @ X26)=(X55 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))))))&((hoasinduction_no_psi_cond_lthm)<=>(![X66:subst > term > subst > $o]:(~(![X4:term > $o]:(~(![X7:term]:(((X4 @ X7)<=>(X66 @ id @ X7 @ id)))))))=>(![X1:term > $o, X44:term]:((~(![X2:term]:((~((var @ X2))|(X1 @ X2))))|(X1 @ X44)|~(![X2:term]:(((X1 @ (lam @ X2))|~(![X8:term]:((~((X1 @ X8))|(X1 @ (sub @ X2 @ (push @ X8 @ id)))))))))|~(![X2:term, X8:term]:(((X1 @ (ap @ X2 @ X8))|~((X1 @ X8))|~((X1 @ X2)))))))=>((![X67:subst > term > subst > $o, X41:term]:((~(![X9:subst > term > term]:((~(![X2:term]:(((X67 @ id @ (X9 @ id @ X2) @ id)|~((X67 @ id @ X2 @ id)))))|(X67 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26))))))))|(X67 @ id @ X41 @ id)|~(![X2:term, X8:term]:(((X67 @ id @ (ap @ (sub @ X2 @ id) @ X8) @ id)|~((X67 @ id @ X8 @ id))|~((X67 @ id @ X2 @ id)))))))<=![X68:subst > term > subst > $o, X4:term > $o, X34:term]:((~(![X9:subst > term > term]:((~(![X2:term]:((~((X68 @ id @ X2 @ id))|(X68 @ id @ (X9 @ id @ X2) @ id))))|(X68 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26))))))))|~(![X8:term]:(((X4 @ (sub @ X34 @ (push @ X8 @ id)))|~((X4 @ X8)))))|(X4 @ (lam @ X34))|~(![X7:term]:(((X4 @ X7)<=>(X68 @ id @ X7 @ id)))))))<=![X2:term]:(((X2)=(sub @ X2 @ id))))))))&((![X1:term > $o, X44:term]:((~(![X2:term]:((~((var @ X2))|(X1 @ X2))))|(X1 @ X44)|~(![X2:term]:(((X1 @ (lam @ X2))|~(![X8:term]:((~((X1 @ X8))|(X1 @ (sub @ X2 @ (push @ X8 @ id)))))))))|~(![X2:term, X8:term]:(((X1 @ (ap @ X2 @ X8))|~((X1 @ X8))|~((X1 @ X2)))))))=>((![X69:subst > term > subst > $o, X50:term]:((~(![X2:term]:(((X69 @ id @ X2 @ id)|~((var @ (sub @ X2 @ id))))))|~(![X2:term, X8:term]:(((X69 @ id @ (ap @ (sub @ X2 @ id) @ X8) @ id)|~((X69 @ id @ X8 @ id))|~((X69 @ id @ X2 @ id)))))|(X69 @ id @ X50 @ id)|~(![X9:subst > term > term]:(((X69 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X2:term]:((~((X69 @ id @ X2 @ id))|(X69 @ id @ (X9 @ id @ X2) @ id))))|~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26))))))))|~(![X3:subst, X2:term, X26:subst, X29:subst]:(((X69 @ X3 @ X2 @ (comp @ X29 @ X26))|~((X69 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26)))))|~(![X3:subst, X2:term, X26:subst, X29:subst]:((~((X69 @ X3 @ X2 @ (comp @ X29 @ X26)))|(X69 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26))))))<=![X70:subst > term > subst > $o, X28:term]:((~(![X3:subst, X2:term, X26:subst, X29:subst]:((~((X70 @ X3 @ X2 @ (comp @ X29 @ X26)))|(X70 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26))))|(X70 @ id @ (lam @ X28) @ id)|~(![X8:term]:(((X70 @ id @ (sub @ X28 @ (push @ X8 @ id)) @ id)|~((X70 @ id @ X8 @ id)))))|~(![X9:subst > term > term]:(((X70 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X2:term]:(((X70 @ id @ (X9 @ id @ X2) @ id)|~((X70 @ id @ X2 @ id)))))|~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26))))))))|~(![X3:subst, X2:term, X26:subst, X29:subst]:(((X70 @ X3 @ X2 @ (comp @ X29 @ X26))|~((X70 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26))))))))<=![X71:subst > term > subst > $o, X64:term, X65:term]:((~(![X3:subst, X2:term, X26:subst, X29:subst]:((~((X71 @ X3 @ X2 @ (comp @ X29 @ X26)))|(X71 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26))))|~(![X3:subst, X2:term, X26:subst, X29:subst]:((~((X71 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26))|(X71 @ X3 @ X2 @ (comp @ X29 @ X26)))))|~((X71 @ id @ X65 @ id))|(X71 @ id @ (ap @ X64 @ X65) @ id)|~((X71 @ id @ X64 @ id))|~(![X2:term, X8:term]:(((X71 @ id @ (ap @ (sub @ X2 @ id) @ X8) @ id)|~((X71 @ id @ X8 @ id))|~((X71 @ id @ X2 @ id)))))))))<=>(hoasinduction_lthm)))&(![X8:term]:(~(![X9:subst > term > term]:(~(![X2:term, X3:subst]:(((sub @ X8 @ (push @ X2 @ X3))=(X9 @ X3 @ X2)))))))<=>(hoasinduction_lem3v2_f_lthm)))&(pushprop_lthm_orig))&(![X2:term, X8:term, X10:term, X11:term]:((((X2)=(X8))|((ap @ (sub @ X2 @ id) @ X10)!=(ap @ (sub @ X8 @ id) @ X11))))<=>(hoasapinj1)))&(hoasapnotvar_gthm))&((induction2lem)<=>![X1:term > $o, X13:term, X14:subst]:((~(![X2:term, X8:term]:((~((X1 @ X8))|(X1 @ (ap @ X2 @ X8))|~((X1 @ X2)))))|~(![X2:term]:(((X1 @ (lam @ X2))|~(![X8:term]:((~((X1 @ X8))|(X1 @ (sub @ X2 @ (push @ X8 @ id)))))))))|(X1 @ (sub @ X13 @ X14))|~(![X8:term]:((~((var @ X8))|(X1 @ (sub @ X8 @ X14)))))))))&(hoasinduction_lem1v2))&(axmap))&(pushprop_lem1_gthm))&~((var @ (d2term @ d_one))))&((hoasinduction_p_and_p_prime)=(^[X72:subst > term > subst > $o, X4:term > $o]:(![X7:term]:((((X4 @ X7))<=>((X72 @ id @ X7 @ id))))))))&((hoaslam)=(^[X73:subst, X74:subst > term > term]:(d2term @ d_one))))&((comp @ (d2subst @ d_id) @ (d2subst @ d_id))=(d2subst @ d_id)))&((sh)=(d2subst @ d_id)))&((id)=(d2subst @ d_id)))&((sub @ (d2term @ d_one) @ (d2subst @ d_id))=(d2term @ d_one)))&![X75:d_subst, X76:d_subst]:((((d2subst @ X75)=(d2subst @ X76))=>((X75)=(X76)))))&![X6:d_subst]:(((X6)=(d_id))))&![X77:d_term, X78:d_term]:((((X77)=(X78))<=((d2term @ X77)=(d2term @ X78)))))&![X79:d_term]:(((X79)=(d_one))))&![X80:term]:(?[X79:d_term]:(((X80)=(d2term @ X79))))), file('/export/starexec/sandbox/tmp/tmp.BWUfY4Bu2F/E---3.1_4003794.p', alg444_1)). 0.29/0.89 thf(pushprop_lem0, conjecture, ((pushprop_lem0)<=>![X1:term > $o, X2:term, X3:subst]:(?[X4:term > $o]:((pushprop_p_and_p_prime @ X2 @ X3 @ X1 @ X4)))), file('/export/starexec/sandbox/tmp/tmp.BWUfY4Bu2F/E---3.1_4003794.p', pushprop_lem0)). 0.29/0.89 thf(c_0_2, plain, ((epred1_0)<=>(![X1:term > $o, X12:term]:((~(![X2:term]:(((X1 @ (lam @ X2))|~((X1 @ X2)))))|(X1 @ X12)|~(![X2:term, X8:term]:((~((X1 @ X2))|~((X1 @ X8))|(X1 @ (ap @ X2 @ X8)))))|~(![X2:term]:(((X1 @ X2)|~(var @ X2))))))=>![X1:term > $o, X13:term, X14:subst]:((~(![X2:term]:((~(![X8:term]:(((X1 @ (sub @ X2 @ (push @ X8 @ id)))|~((X1 @ X8)))))|(X1 @ (lam @ X2)))))|(X1 @ (sub @ X13 @ X14))|~(![X8:term]:((~(var @ X8)|(X1 @ (sub @ X8 @ X14)))))|~(![X2:term, X8:term]:(((X1 @ (ap @ X2 @ X8))|~((X1 @ X8))|~((X1 @ X2))))))))), introduced(definition)). 0.29/0.89 thf(c_0_3, plain, ((epred2_0)<=>(![X36:subst > term > subst > $o, 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X28:term]:((~(![X3:subst, X2:term, X26:subst, X29:subst]:((~((X27 @ X3 @ X2 @ (comp @ X29 @ X26)))|(X27 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26))))|~(![X3:subst, X2:term, X26:subst, X29:subst]:(((X27 @ X3 @ X2 @ (comp @ X29 @ X26))|~((X27 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26)))))|~(![X8:term]:(((X27 @ id @ (sub @ X28 @ (push @ X8 @ id)) @ id)|~((X27 @ id @ X8 @ id)))))|(X27 @ id @ (lam @ X28) @ id)|~(![X9:subst > term > term]:((~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))|~(![X2:term]:((~((X27 @ id @ X2 @ id))|(X27 @ id @ (X9 @ id @ X2) @ id))))|(X27 @ id @ (lam @ (X9 @ sh @ one)) @ id))))))))&(termmset_lthm))&((![X2:term, X3:subst]:(((X2)=(sub @ one @ (push @ X2 @ X3))))=>![X1:term > $o, X4:term > $o, X2:term, X3:subst]:((~((X1 @ X2))|~(![X7:term]:(((X4 @ X7)<=>(X1 @ (sub @ X7 @ (push @ X2 @ X3))))))|(X4 @ one))))<=>(pushprop_lem1v2_lthm)))&(hoasapnotvar))&(pushprop_lem3v2_lthm))&(pushprop_lem1v2_gthm))&(hoaslamnotvar_gthm))&(hoasinduction_lem3a_gthm))&(axclos))&(axassoc))&(![X30:subst > term > subst > $o, X4:term > $o, X31:term, X32:term]:((~(![X3:subst, X2:term, X26:subst, X29:subst]:((~((X30 @ X3 @ X2 @ (comp @ X29 @ X26)))|(X30 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26))))|~(![X3:subst, X2:term, X26:subst, X29:subst]:((~((X30 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26))|(X30 @ X3 @ X2 @ (comp @ X29 @ X26)))))|~(![X7:term]:(((X4 @ X7)<=>(X30 @ id @ X7 @ id))))|~((X4 @ X32))|(X4 @ (ap @ X31 @ X32))|~((X4 @ X31))|~(![X2:term, X8:term]:((~((X30 @ id @ X8 @ id))|(X30 @ id @ (ap @ (sub @ X2 @ id) @ X8) @ id)|~((X30 @ id @ X2 @ id)))))))<=>(hoasinduction_lem2v2)))&(pushprop_lthm))&((apinj1)<=>![X2:term, X8:term, X10:term, X11:term]:((((X2)=(X8))|((ap @ X2 @ X10)!=(ap @ X8 @ X11))))))&(![X33:subst > term > subst > $o, X4:term > $o, X34:term]:((~(![X9:subst > term > term]:(((X33 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X2:term]:(((X33 @ id @ (X9 @ id @ X2) @ id)|~((X33 @ id @ X2 @ id)))))|~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26))))))))|~(![X7:term]:(((X4 @ X7)<=>(X33 @ id @ X7 @ id))))|(X4 @ (lam @ X34))|~(![X8:term]:(((X4 @ (sub @ X34 @ (push @ X8 @ id)))|~((X4 @ X8)))))))<=>(hoasinduction_lem3v2a)))&((hoasapinj1_lthm)<=>(![X2:term]:(((X2)=(sub @ X2 @ id)))=>(![X2:term, X8:term, X10:term, X11:term]:((((X2)=(X8))|((ap @ X2 @ X10)!=(ap @ X8 @ X11))))=>![X2:term, X8:term, X10:term, X11:term]:((((ap @ (sub @ X2 @ id) @ X10)!=(ap @ (sub @ X8 @ id) @ X11))|((X2)=(X8))))))))&((axvarcons)<=>![X2:term, X3:subst]:(((X2)=(sub @ one @ (push @ X2 @ X3))))))&((axscons)<=>![X3:subst]:(((X3)=(push @ (sub @ one @ X3) @ (comp @ sh @ X3))))))&(hoasinduction_lem2v2_gthm))&((axidr)<=>![X3:subst]:(((X3)=(comp @ X3 @ id)))))&(![X1:term > $o, X35:term > $o, X2:term, X3:subst, X8:term]:((~((X1 @ X2))|(X35 @ (sub @ X2 @ (push @ X8 @ X3)))))<=>(pushprop_lem1)))&((![X2:term]:(((X2)=(sub @ X2 @ id)))=>(epred2_0))<=>(hoasinduction_lem3_lthm)))&(![X1:term > $o, X2:term, X3:subst]:(~(![X4:term > $o]:(~(![X7:term]:(((X4 @ X7)<=>(X1 @ (sub @ X7 @ (push @ X2 @ X3)))))))))<=>(pushprop_lem0)))&(pushprop_gthm))&((hoasinduction_lem3v2a_lthm)<=>(![X8:term]:(~(![X9:subst > term > term]:(~(![X2:term, X3:subst]:(((sub @ X8 @ (push @ X2 @ X3))=(X9 @ X3 @ X2)))))))=>(![X2:term]:(((X2)=(sub @ X2 @ id)))=>![X38:subst > term > subst > $o, X4:term > $o, X34:term]:((~(![X9:subst > term > term]:(((X38 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X2:term]:(((X38 @ id @ (X9 @ id @ X2) @ id)|~((X38 @ id @ X2 @ id)))))|~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26))))))))|(X4 @ (lam @ X34))|~(![X8:term]:((~((X4 @ X8))|(X4 @ (sub @ X34 @ (push @ X8 @ id))))))|~(![X7:term]:(((X4 @ X7)<=>(X38 @ id @ X7 @ id))))))))))&(hoasinduction_lem2_lthm))&(hoasinduction_lem1_lthm))&~(lamnotap))&(hoasapinj1_gthm))&((axidl)<=>![X3:subst]:(((X3)=(comp @ id @ X3)))))&((hoasinduction_lem0_lthm)<=>![X39:subst > term > subst > $o]:(~(![X4:term > $o]:(~(![X7:term]:(((X4 @ X7)<=>(X39 @ id @ X7 @ id)))))))))&((substmonoid_lthm)<=>(![X3:subst]:(((X3)=(comp @ id @ X3)))=>(![X3:subst]:(((X3)=(comp @ X3 @ id)))=>(![X3:subst]:(((X3)=(comp @ id @ X3)))&![X3:subst]:(((X3)=(comp @ X3 @ id))))))))&(hoasinduction_lem3_gthm))&(lamnotvar))&(hoasinduction_lem1_gthm))&(![X40:subst > term > subst > $o, X41:term]:((~(![X2:term, X8:term]:(((X40 @ id @ (ap @ (sub @ X2 @ id) @ X8) @ id)|~((X40 @ id @ X8 @ id))|~((X40 @ id @ X2 @ id)))))|(X40 @ id @ X41 @ id)|~(![X9:subst > term > term]:((~(![X2:term]:((~((X40 @ id @ X2 @ id))|(X40 @ id @ (X9 @ id @ X2) @ id))))|(X40 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26))))))))))<=>(hoasinduction_no_psi_cond)))&(induction2_gthm))&(pushprop_lem2v2_lthm))&((hoaslamnotap)<=>![X9:subst > term > term, X42:term, X43:term]:((~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))|((lam @ (X9 @ sh @ one))!=(ap @ (sub @ X42 @ id) @ X43))))))&(![X1:term > $o, X44:term]:((~(![X2:term]:((~(var @ X2)|(X1 @ X2))))|~(![X2:term]:((~(![X8:term]:(((X1 @ (sub @ X2 @ (push @ X8 @ id)))|~((X1 @ X8)))))|(X1 @ (lam @ X2)))))|(X1 @ X44)|~(![X2:term, X8:term]:((~((X1 @ X2))|(X1 @ (ap @ X2 @ X8))|~((X1 @ X8)))))))<=>(induction2)))&(pushprop_lem3v2))&(pushprop_lem2v2_gthm))&((pushprop_lem1_lthm)<=>(![X2:term, X3:subst]:(((X2)=(sub @ one @ (push @ X2 @ X3))))=>(![X2:term, X3:subst]:(((X3)=(comp @ sh @ (push @ X2 @ X3))))=>![X1:term > $o, X45:term > $o, X2:term, X3:subst, X8:term]:(((X45 @ (sub @ X2 @ (push @ X8 @ X3)))|~((X1 @ X2))))))))&((epred3_0)<=>(hoasinduction_lem3v2)))&((axshiftcons)<=>![X2:term, X3:subst]:(((X3)=(comp @ sh @ (push @ X2 @ X3))))))&(![X1:term > $o, X2:term, X3:subst]:(~(![X4:term > $o]:(~(![X7:term]:(((X4 @ X7)<=>(X1 @ (sub @ X7 @ (push @ X2 @ X3)))))))))<=>(pushprop_lem0_lthm)))&(hoasapnotvar_lthm))&((axvarid)<=>![X2:term]:(((X2)=(sub @ X2 @ id)))))&((hoasinduction_lthm_3)<=>(![X51:subst > term > subst > $o]:(~(![X4:term > $o]:(~(![X7:term]:(((X4 @ X7)<=>(X51 @ id @ X7 @ id)))))))=>(epred5_0))))&((hoasinduction_lem3v2_lthm)<=>(![X2:term]:(((X2)=(sub @ X2 @ id)))=>(epred6_0))))&(![X2:term]:(((X2)=(sub @ X2 @ id)))<=>(termmset)))&(ulamvarsh))&(substmonoid_gthm))&~(hoasvar @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id)))&((hoasinduction_lem3a)<=>![X53:subst > term > subst > $o, X54:term]:((~(![X9:subst > term > term]:((~(![X2:term]:((~((X53 @ id @ X2 @ id))|(X53 @ id @ (X9 @ id @ X2) @ id))))|(X53 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26))))))))|(X53 @ id @ (lam @ X54) @ id)|~(![X8:term]:(((X53 @ id @ (sub @ X54 @ (push @ X8 @ id)) @ id)|~((X53 @ id @ X8 @ id)))))))))&((![X3:subst]:(((X3)=(comp @ X3 @ id)))&![X3:subst]:(((X3)=(comp @ id @ X3))))<=>(substmonoid)))&((hoasinduction_lem3b)<=>![X8:term]:(~(![X9:subst > term > term]:(((X9 @ sh @ one)!=(sub @ X8 @ (push @ one @ sh))))))))&(hoasinduction_lem2_gthm))&(pushprop))&((![X2:term]:(((X2)=(sub @ X2 @ id)))=>(epred7_0))<=>(induction2_lthm)))&(hoaslaminj_gthm))&(hoaslamnotvar))&(hoasapinj2_gthm))&(axabs))&((laminj)<=>![X2:term, X8:term]:((((lam @ X2)!=(lam @ X8))|((X2)=(X8))))))&((![X2:term, X3:subst]:(((X2)=(sub @ one @ (push @ X2 @ X3))))=>(![X2:term, X3:subst]:(((X3)=(comp @ sh @ (push @ X2 @ X3))))=>(![X2:term, X8:term]:((((X2)=(X8))|((lam @ X2)!=(lam @ X8))))=>![X9:subst > term > term, X55:subst > term > term, X56:subst, X57:term]:((~(![X3:subst, X2:term, X26:subst]:(((sub @ (X55 @ X3 @ X2) @ X26)=(X55 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))|((lam @ (X9 @ sh @ one))!=(lam @ (X55 @ sh @ one)))|((X9 @ X56 @ X57)=(X55 @ X56 @ X57))|~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26))))))))))<=>(hoaslaminj_lthm)))&((hoasapinj2_lthm)<=>(![X2:term, X8:term, X10:term, X11:term]:((((ap @ X2 @ X10)!=(ap @ X8 @ X11))|((X10)=(X11))))=>![X2:term, X8:term, X10:term, X11:term]:((((ap @ (sub @ X2 @ id) @ X10)!=(ap @ (sub @ X8 @ id) @ X11))|((X10)=(X11)))))))&((apinj2)<=>![X2:term, X8:term, X10:term, X11:term]:((((ap @ X2 @ X10)!=(ap @ X8 @ X11))|((X10)=(X11))))))&(pushprop_lem2v2))&(hoasinduction_lem3b_gthm))&(hoaslamnotap_gthm))&(![X58:subst > term > subst > $o, X25:term]:((~(![X8:term]:(((X58 @ id @ (sub @ X25 @ (push @ X8 @ id)) @ id)|~((X58 @ id @ X8 @ id)))))|(X58 @ id @ (lam @ (sub @ X25 @ (push @ one @ sh))) @ id)|~(![X9:subst > term > term]:((~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))|(X58 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X2:term]:(((X58 @ id @ (X9 @ id @ X2) @ id)|~((X58 @ id @ X2 @ id))))))))))<=>(hoasinduction_lem3aa)))&(termmset_gthm))&((hoasinduction_lem3a_lthm)<=>(![X2:term]:(((X2)=(sub @ X2 @ id)))=>(![X59:subst > term > subst > $o, X25:term]:((~(![X8:term]:((~((X59 @ id @ X8 @ id))|(X59 @ id @ (sub @ X25 @ (push @ X8 @ id)) @ id))))|(X59 @ id @ (lam @ (sub @ X25 @ (push @ one @ sh))) @ id)|~(![X9:subst > term > term]:((~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))|~(![X2:term]:((~((X59 @ id @ X2 @ id))|(X59 @ id @ (X9 @ id @ X2) @ id))))|(X59 @ id @ (lam @ (X9 @ sh @ one)) @ id))))))=>![X60:subst > term > subst > $o, X54:term]:(((X60 @ id @ (lam @ X54) @ id)|~(![X8:term]:((~((X60 @ id @ X8 @ id))|(X60 @ id @ (sub @ X54 @ (push @ X8 @ id)) @ id))))|~(![X9:subst > term > term]:((~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))|(X60 @ id @ (lam @ (X9 @ sh @ one)) @ id)|~(![X2:term]:(((X60 @ id @ (X9 @ id @ X2) @ id)|~((X60 @ id @ X2 @ id))))))))))))))&(![X1:term > $o, X12:term]:((~(![X2:term, X8:term]:(((X1 @ (ap @ X2 @ X8))|~((X1 @ X8))|~((X1 @ X2)))))|~(![X2:term]:((~((X1 @ X2))|(X1 @ (lam @ X2)))))|(X1 @ X12)|~(![X2:term]:((~(var @ X2)|(X1 @ X2))))))<=>(induction)))&(ulamvarind))&(![X8:term]:(~(![X9:subst > term > term]:(((X9 @ sh @ one)!=(sub @ X8 @ (push @ one @ sh))))))<=>(hoasinduction_lem3b_lthm)))&(hoaslamnotvar_lthm))&(axapp))&(hoasinduction_gthm))&((hoasinduction)<=>![X61:subst > term > subst > $o, X50:term]:(((epred8_2 @ X61 @ X50)|~(![X3:subst, X2:term, X26:subst, X29:subst]:((~((X61 @ X3 @ X2 @ (comp @ X29 @ X26)))|(X61 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26))))))))&(![X62:subst > term > subst > $o]:(~(![X4:term > $o]:(~(![X7:term]:(((X4 @ X7)<=>(X62 @ id @ X7 @ id)))))))<=>(hoasinduction_lem0)))&(hoaslamnotap_lthm))&(hoasinduction_lem1))&(![X63:subst > term > subst > $o, X64:term, X65:term]:((~(![X3:subst, X2:term, X26:subst, X29:subst]:((~((X63 @ X3 @ X2 @ (comp @ X29 @ X26)))|(X63 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26))))|(X63 @ id @ (ap @ X64 @ X65) @ id)|~((X63 @ id @ X65 @ id))|~((X63 @ id @ X64 @ id))|~(![X2:term, X8:term]:((~((X63 @ id @ X2 @ id))|(X63 @ id @ (ap @ (sub @ X2 @ id) @ X8) @ id)|~((X63 @ id @ X8 @ id)))))|~(![X3:subst, X2:term, X26:subst, X29:subst]:(((X63 @ X3 @ X2 @ (comp @ X29 @ X26))|~((X63 @ (comp @ X3 @ X29) @ (sub @ X2 @ X29) @ X26)))))))<=>(hoasinduction_lem2)))&(induction2lem_gthm))&((hoaslaminj)<=>![X9:subst > term > term, X55:subst > term > term, X56:subst, X57:term]:((~(![X3:subst, X2:term, X26:subst]:(((sub @ (X9 @ X3 @ X2) @ X26)=(X9 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))|((X9 @ X56 @ X57)=(X55 @ X56 @ X57))|((lam @ (X9 @ sh @ one))!=(lam @ (X55 @ sh @ one)))|~(![X3:subst, X2:term, X26:subst]:(((sub @ (X55 @ X3 @ X2) @ X26)=(X55 @ (comp @ X3 @ X26) @ (sub @ X2 @ X26)))))))))&((hoasinduction_no_psi_cond_lthm)<=>(![X66:subst > term > subst > $o]:(~(![X4:term > $o]:(~(![X7:term]:(((X4 @ X7)<=>(X66 @ id @ X7 @ id)))))))=>(![X1:term > $o, X44:term]:((~(![X2:term]:((~(var @ X2)|(X1 @ X2))))|(X1 @ X44)|~(![X2:term]:(((X1 @ (lam @ X2))|~(![X8:term]:((~((X1 @ X8))|(X1 @ (sub @ X2 @ (push @ X8 @ id)))))))))|~(![X2:term, X8:term]:(((X1 @ (ap @ X2 @ X8))|~((X1 @ X8))|~((X1 @ X2)))))))=>(![X2:term]:(((X2)=(sub @ X2 @ id)))=>(epred9_0))))))&((epred12_0)<=>(hoasinduction_lthm)))&(![X8:term]:(~(![X9:subst > term > term]:(~(![X2:term, X3:subst]:(((sub @ X8 @ (push @ X2 @ X3))=(X9 @ X3 @ X2)))))))<=>(hoasinduction_lem3v2_f_lthm)))&(pushprop_lthm_orig))&(![X2:term, X8:term, X10:term, X11:term]:((((X2)=(X8))|((ap @ (sub @ X2 @ id) @ X10)!=(ap @ (sub @ X8 @ id) @ X11))))<=>(hoasapinj1)))&(hoasapnotvar_gthm))&((induction2lem)<=>![X1:term > $o, X13:term, X14:subst]:((~(![X2:term, X8:term]:((~((X1 @ X8))|(X1 @ (ap @ X2 @ X8))|~((X1 @ X2)))))|~(![X2:term]:(((X1 @ (lam @ X2))|~(![X8:term]:((~((X1 @ X8))|(X1 @ (sub @ X2 @ (push @ X8 @ id)))))))))|(X1 @ (sub @ X13 @ X14))|~(![X8:term]:((~(var @ X8)|(X1 @ (sub @ X8 @ X14)))))))))&(hoasinduction_lem1v2))&(axmap))&(pushprop_lem1_gthm))&~(var @ (d2term @ d_one)))&![X629:subst > term > subst > $o, X630:term > $o]:(((hoasinduction_p_and_p_prime @ X629 @ X630)<=>![X7:term]:(((X630 @ X7)<=>(X629 @ id @ X7 @ id))))))&![X631:subst, X632:subst > term > term]:(((hoaslam @ X631 @ X632)=(d2term @ d_one))))&((comp @ (d2subst @ d_id) @ (d2subst @ d_id))=(d2subst @ d_id)))&((sh)=(d2subst @ d_id)))&((id)=(d2subst @ d_id)))&((sub @ (d2term @ d_one) @ (d2subst @ d_id))=(d2term @ d_one)))&![X75:d_subst, X76:d_subst]:((((d2subst @ X75)=(d2subst @ X76))=>((X75)=(X76)))))&![X6:d_subst]:(((X6)=(d_id))))&![X77:d_term, X78:d_term]:((((d2term @ X77)=(d2term @ X78))=>((X77)=(X78)))))&![X79:d_term]:(((X79)=(d_one))))&![X80:term]:(?[X79:d_term]:(((X80)=(d2term @ X79))))), inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(apply_def,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[inference(fof_simplification,[status(thm)],[alg444_1])])]), c_0_2]), c_0_3]), c_0_4]), c_0_5]), c_0_6]), c_0_7]), c_0_8]), c_0_9]), c_0_10])). 0.29/0.89 thf(c_0_12, plain, ![X641:subst, X643:term, X644:subst, X645:term > $o, X646:term > $o, X647:term, X648:term, X649:term, X650:subst, X651:term > $o, X652:term > $o, X658:term, X659:term > $o, X660:term > $o, X661:term, X662:subst, X666:term, X667:term, X668:term, X670:term, X671:subst, X673:subst > term > term, X680:term, X681:term, X682:term, X683:term, X684:term, X685:subst, X686:term, X687:subst, X688:subst, X696:term, X697:subst > term > term, X698:term, X706:subst > term > subst > $o, X707:term, X711:subst, X712:term, X713:subst, X714:subst, X715:term, X716:subst, X717:term, X720:subst > term > term, X725:term, X726:subst > term > subst > $o, X727:term, X729:subst, X730:term, X731:subst, X732:term, X734:subst > term > subst > $o, X735:term, X746:subst, X747:term, X748:subst, X749:term, X752:subst, X753:term, X754:subst, X755:subst, X756:subst, X757:term, X758:subst, X759:subst, X760:term, X761:subst > term > term, X766:term, X767:subst, X772:term, X775:term > $o, X776:term > $o, X777:term, X778:subst, X784:subst, X785:term, X786:subst, X787:subst, X788:subst, X789:term, X790:subst, X791:subst, X792:term, X793:term, X794:term, X795:subst > term > subst > $o, X796:term > $o, X797:term, X798:term, X810:term, X811:term, X812:term, X813:term, X821:subst > term > term, X826:term, X827:term, X828:subst > term > subst > $o, X829:term > $o, X830:term, X832:term, X833:subst, X834:term, X835:subst, X843:term, X844:term, X845:term, X846:term, X847:term, X848:term, X849:term, X850:term, X851:term, X856:term, X857:subst, X860:subst, X862:subst, X869:term > $o, X870:term > $o, X871:term, X872:subst, X873:term, X874:term, X879:term > $o, X881:term > $o, X882:term, X883:subst, X885:term, X886:term, X888:subst > term > term, X892:subst > term > subst > $o, X893:term > $o, X894:term, X896:term, X897:subst, X898:term, X899:subst, X902:term, X904:term, X905:subst, X906:term, X910:subst > term > term, X915:term, X916:term, X917:subst, X919:subst > term > subst > $o, X921:term, X922:term, X924:term > $o, X928:subst, X929:subst, X930:subst, X931:subst, X936:term, X937:term, X938:subst > term > term, X943:subst > term > subst > $o, X946:term, X948:term, X949:subst, X950:term, X951:subst, X952:subst > term > term, X956:term, X957:term, X961:subst, X962:term, X963:subst, X966:term, X967:term, X969:term, X970:term, X971:term > $o, X974:term, X975:term, X982:term > $o, X983:term > $o, X984:term, X985:subst, X986:term, X987:term, X988:subst, X989:term, X990:subst, X996:term, X997:subst, X1003:term > $o, X1005:term > $o, X1006:term, X1007:subst, X1009:term, X1010:term, X1011:term, X1014:term > $o, X1016:subst > term > subst > $o, X1018:term, X1019:term, X1021:term, X1023:term, X1024:subst > term > subst > $o, X1025:term, X1027:term, X1028:subst, X1029:term, X1030:subst, X1034:subst > term > term, X1039:term, X1042:subst, X1043:subst, X1044:term, X1047:subst > term > term, X1048:term, X1050:term, X1051:term, X1054:term, X1055:subst, X1056:term, X1057:subst, X1058:term, X1059:term, X1064:subst, X1065:term, X1066:subst, X1067:subst, X1068:term, X1069:subst, X1076:subst > term > term, X1077:subst > term > term, X1081:subst, X1082:term, X1090:term, X1091:term, X1092:term, X1093:term, X1094:term, X1095:term, X1096:term, X1097:term, X1102:term, X1103:term, X1104:term, X1105:term, X1112:term, X1113:subst > term > term, X1118:subst > term > subst > $o, X1119:term, X1122:subst, X1123:term, X1124:subst, X1125:term, X1129:term, X1130:subst > term > term, X1135:subst > term > subst > $o, X1136:term, X1139:subst, X1140:term, X1141:subst, X1142:term, X1143:term, X1144:subst > term > subst > $o, X1145:term, X1148:subst, X1149:term, X1150:subst, X1151:term, X1154:term, X1155:subst > term > term, X1162:term, X1163:term, X1164:term, X1165:term, X1166:term > $o, X1170:term, X1173:subst > term > term, X1174:term, X1176:subst > term > subst > $o, X1177:term, X1184:subst, X1185:term, X1186:subst, X1187:subst, X1189:term > $o, X1191:subst > term > subst > $o, X1193:term, X1194:term, X1198:subst, X1199:term, X1200:subst, X1201:subst, X1202:term, X1203:term, X1204:subst, X1205:term, X1206:subst, X1207:subst, X1208:subst > term > subst > $o, X1209:term, X1210:term, X1221:subst > term > term, X1222:subst > term > term, X1226:subst, X1227:term, X1235:subst, X1236:term, X1237:subst, X1238:subst, X1239:term, X1240:subst, X1242:term > $o, X1246:term, X1247:term, X1249:term, X1250:term, X1252:subst > term > subst > $o, X1254:term, X1255:term, X1256:term > $o, X1258:term, X1260:term, X1263:term, X1265:subst > term > term, X1268:term, X1270:term, X1271:subst, X1276:term, X1277:term, X1278:term, X1279:term, X1280:term > $o, X1281:term, X1282:subst, X1286:term, X1291:term, X1292:term, X1293:term, X1295:term, X1296:subst > term > subst > $o, X1297:term > $o, X1298:term, X1299:term, X1300:subst > term > subst > $o, X1301:term > $o, X1303:subst, X1304:subst > term > term, X1305:d_subst, X1306:d_subst, X1307:d_subst, X1308:d_term, X1309:d_term, X1310:d_term, X1311:term]:((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((X641)=(d2subst @ (esk3_1 @ X641)))&((one)=(d2term @ d_one)))&((ap @ (d2term @ d_one) @ (d2term @ d_one))=(d2term @ d_one)))&((lam @ (d2term @ d_one))=(d2term @ d_one)))&((push @ (d2term @ d_one) @ (d2subst @ d_id))=(d2subst @ d_id)))&((hoasap @ (d2subst @ d_id) @ (d2term @ d_one) @ (d2subst @ d_id) @ (d2term @ d_one))=(d2term @ d_one)))&(((~(X646 @ X647)|(X645 @ (sub @ X647 @ (push @ X643 @ X644)))|~(pushprop_p_and_p_prime @ X643 @ X644 @ X645 @ X646))&(~(X645 @ (sub @ X648 @ (push @ X643 @ X644)))|(X646 @ X648)|~(pushprop_p_and_p_prime @ X643 @ X644 @ X645 @ X646)))&((~(X652 @ (esk4_4 @ X649 @ X650 @ X651 @ X652))|~(X651 @ (sub @ (esk4_4 @ X649 @ X650 @ X651 @ X652) @ (push @ X649 @ X650)))|(pushprop_p_and_p_prime @ X649 @ X650 @ X651 @ X652))&((X652 @ (esk4_4 @ X649 @ X650 @ X651 @ X652))|(X651 @ (sub @ (esk4_4 @ X649 @ X650 @ X651 @ X652) @ (push @ X649 @ X650)))|(pushprop_p_and_p_prime @ X649 @ X650 @ X651 @ X652)))))&(((((~(epred16_0 @ X658)|(epred15_0 @ (sub @ X658 @ (push @ esk5_0 @ esk6_0)))|(pushprop_lem1v2))&(~(epred15_0 @ (sub @ X658 @ (push @ esk5_0 @ esk6_0)))|(epred16_0 @ X658)|(pushprop_lem1v2)))&(~(epred16_0 @ one)|(pushprop_lem1v2)))&((epred15_0 @ esk5_0)|(pushprop_lem1v2)))&((~(X660 @ (esk7_4 @ X659 @ X660 @ X661 @ X662))|~(X659 @ (sub @ (esk7_4 @ X659 @ X660 @ X661 @ X662) @ (push @ X661 @ X662)))|(X660 @ one)|~(X659 @ X661)|~(pushprop_lem1v2))&((X660 @ (esk7_4 @ X659 @ X660 @ X661 @ X662))|(X659 @ (sub @ (esk7_4 @ X659 @ X660 @ X661 @ X662) @ (push @ X661 @ X662)))|(X660 @ one)|~(X659 @ X661)|~(pushprop_lem1v2)))))&(pushprop_lem0_gthm))&(((((esk8_0)!=(esk9_0))|(shinj))&(((sub @ esk8_0 @ sh)=(sub @ esk9_0 @ sh))|(shinj)))&(~(shinj)|(((X666)=(X667))|((sub @ X666 @ sh)!=(sub @ X667 @ sh))))))&(hoasinduction_lem1v2_gthm))&((~(hoasinduction_lem3v2_f)|((sub @ X668 @ (push @ X670 @ X671))=(esk10_1 @ X668 @ X671 @ X670)))&(((sub @ esk11_0 @ (push @ (esk12_1 @ X673) @ (esk13_1 @ X673)))!=(X673 @ (esk13_1 @ X673) @ (esk12_1 @ X673)))|(hoasinduction_lem3v2_f))))&(axvarshift))&(((((ap @ (sub @ esk14_0 @ id) @ esk16_0)=(ap @ (sub @ esk15_0 @ id) @ esk17_0))|(hoasapinj2))&(((esk16_0)!=(esk17_0))|(hoasapinj2)))&(~(hoasapinj2)|(((ap @ (sub @ X680 @ id) @ X682)!=(ap @ (sub @ X681 @ id) @ X683))|((X682)=(X683))))))&~(ulamvar1))&(((((X684)=(sub @ one @ (push @ X684 @ X685)))|(induction2lem_lthm))&((((X687)=(comp @ sh @ (push @ X686 @ X687)))|(induction2lem_lthm))&((((X688)=(comp @ X688 @ id))|(induction2lem_lthm))&(~(epred1_0)|(induction2lem_lthm)))))&(~(induction2lem_lthm)|(((esk18_0)!=(sub @ one @ (push @ esk18_0 @ esk19_0)))|(((esk21_0)!=(comp @ sh @ (push @ esk20_0 @ esk21_0)))|(((esk22_0)!=(comp @ esk22_0 @ id))|(epred1_0)))))))&(hoasinduction_lem3v2_gthm))&(apnotvar))&((((~(epred17_0 @ id @ (lam @ (sub @ esk23_0 @ (push @ one @ sh))) @ id)|(hoasinduction_lem3aaa))&(~(epred17_0 @ id @ X696 @ id)|(epred17_0 @ id @ (sub @ esk23_0 @ (push @ X696 @ id)) @ id)|(hoasinduction_lem3aaa)))&((~(epred17_0 @ id @ (X697 @ id @ (esk30_2 @ X697 @ X698)) @ id)|((epred17_0 @ id @ (lam @ (X697 @ sh @ one)) @ id)|((X697 @ (comp @ (esk24_2 @ X697 @ X698) @ (esk26_2 @ X697 @ X698)) @ (sub @ (esk25_2 @ X697 @ X698) @ (esk26_2 @ X697 @ X698)))!=(sub @ X698 @ (push @ (sub @ (esk25_2 @ X697 @ X698) @ (esk26_2 @ X697 @ X698)) @ (comp @ (esk24_2 @ X697 @ X698) @ (esk26_2 @ X697 @ X698)))))|((sub @ (X697 @ (esk27_2 @ X697 @ X698) @ (esk28_2 @ X697 @ X698)) @ (esk29_2 @ X697 @ X698))!=(sub @ (sub @ X698 @ (push @ (esk28_2 @ X697 @ X698) @ (esk27_2 @ X697 @ X698))) @ (esk29_2 @ X697 @ X698))))|(hoasinduction_lem3aaa))&((epred17_0 @ id @ (esk30_2 @ X697 @ X698) @ id)|((epred17_0 @ id @ (lam @ (X697 @ sh @ one)) @ id)|((X697 @ (comp @ (esk24_2 @ X697 @ X698) @ (esk26_2 @ X697 @ X698)) @ (sub @ (esk25_2 @ X697 @ X698) @ (esk26_2 @ X697 @ X698)))!=(sub @ X698 @ (push @ (sub @ (esk25_2 @ X697 @ X698) @ (esk26_2 @ X697 @ X698)) @ (comp @ (esk24_2 @ X697 @ X698) @ (esk26_2 @ X697 @ X698)))))|((sub @ (X697 @ (esk27_2 @ X697 @ X698) @ (esk28_2 @ X697 @ X698)) @ (esk29_2 @ X697 @ X698))!=(sub @ (sub @ X698 @ (push @ (esk28_2 @ X697 @ X698) @ (esk27_2 @ X697 @ X698))) @ (esk29_2 @ X697 @ X698))))|(hoasinduction_lem3aaa))))&(((((~(X706 @ id @ (lam @ (esk32_1 @ X706 @ sh @ one)) @ id)|((X706 @ id @ (esk31_2 @ X706 @ X707) @ id)|(X706 @ id @ (lam @ (sub @ X707 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa))&(((esk32_1 @ X706 @ (comp @ X711 @ X713) @ (sub @ X712 @ X713))=(sub @ (esk33_1 @ X706) @ (push @ (sub @ X712 @ X713) @ (comp @ X711 @ X713))))|((X706 @ id @ (esk31_2 @ X706 @ X707) @ id)|(X706 @ id @ (lam @ (sub @ X707 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa)))&(((sub @ (esk32_1 @ X706 @ X714 @ X715) @ X716)=(sub @ (sub @ (esk33_1 @ X706) @ (push @ X715 @ X714)) @ X716))|((X706 @ id @ (esk31_2 @ X706 @ X707) @ id)|(X706 @ id @ (lam @ (sub @ X707 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa)))&((X706 @ id @ (esk32_1 @ X706 @ id @ X717) @ id)|~(X706 @ id @ X717 @ id)|((X706 @ id @ (esk31_2 @ X706 @ X707) @ id)|(X706 @ id @ (lam @ (sub @ X707 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa)))&((((~(X706 @ id @ (lam @ (esk32_1 @ X706 @ sh @ one)) @ id)|(~(X706 @ id @ (sub @ X707 @ (push @ (esk31_2 @ X706 @ X707) @ id)) @ id)|(X706 @ id @ (lam @ (sub @ X707 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa))&(((esk32_1 @ X706 @ (comp @ X711 @ X713) @ (sub @ X712 @ X713))=(sub @ (esk33_1 @ X706) @ (push @ (sub @ X712 @ X713) @ (comp @ X711 @ X713))))|(~(X706 @ id @ (sub @ X707 @ (push @ (esk31_2 @ X706 @ X707) @ id)) @ id)|(X706 @ id @ (lam @ (sub @ X707 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa)))&(((sub @ (esk32_1 @ X706 @ X714 @ X715) @ X716)=(sub @ (sub @ (esk33_1 @ X706) @ (push @ X715 @ X714)) @ X716))|(~(X706 @ id @ (sub @ X707 @ (push @ (esk31_2 @ X706 @ X707) @ id)) @ id)|(X706 @ id @ (lam @ (sub @ X707 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa)))&((X706 @ id @ (esk32_1 @ X706 @ id @ X717) @ id)|~(X706 @ id @ X717 @ id)|(~(X706 @ id @ (sub @ X707 @ (push @ (esk31_2 @ X706 @ X707) @ id)) @ id)|(X706 @ id @ (lam @ (sub @ X707 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aaa))))))&(((((~(epred18_0 @ id @ (X720 @ id @ (esk38_1 @ X720)) @ id)|(((sub @ (X720 @ (esk35_1 @ X720) @ (esk36_1 @ X720)) @ (esk37_1 @ X720))!=(X720 @ (comp @ (esk35_1 @ X720) @ (esk37_1 @ X720)) @ (sub @ (esk36_1 @ X720) @ (esk37_1 @ X720))))|(epred18_0 @ id @ (lam @ (X720 @ sh @ one)) @ id))|(hoasinduction_lem3aa_lthm))&((epred18_0 @ id @ (esk38_1 @ X720) @ id)|(((sub @ (X720 @ (esk35_1 @ X720) @ (esk36_1 @ X720)) @ (esk37_1 @ X720))!=(X720 @ (comp @ (esk35_1 @ X720) @ (esk37_1 @ X720)) @ (sub @ (esk36_1 @ X720) @ (esk37_1 @ X720))))|(epred18_0 @ id @ (lam @ (X720 @ sh @ one)) @ id))|(hoasinduction_lem3aa_lthm)))&(~(epred18_0 @ id @ (lam @ (sub @ esk34_0 @ (push @ one @ sh))) @ id)|(hoasinduction_lem3aa_lthm)))&((epred18_0 @ id @ (sub @ esk34_0 @ (push @ X725 @ id)) @ id)|~(epred18_0 @ id @ X725 @ id)|(hoasinduction_lem3aa_lthm)))&((((~(X726 @ id @ (sub @ X727 @ (push @ (esk40_2 @ X726 @ X727) @ id)) @ id)|(((sub @ (esk39_2 @ X726 @ X727 @ X729 @ X730) @ X731)=(esk39_2 @ X726 @ X727 @ (comp @ X729 @ X731) @ (sub @ X730 @ X731)))|(X726 @ id @ (lam @ (sub @ X727 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aa_lthm))&((X726 @ id @ (esk40_2 @ X726 @ X727) @ id)|(((sub @ (esk39_2 @ X726 @ X727 @ X729 @ X730) @ X731)=(esk39_2 @ X726 @ X727 @ (comp @ X729 @ X731) @ (sub @ X730 @ X731)))|(X726 @ id @ (lam @ (sub @ X727 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aa_lthm)))&((~(X726 @ id @ (sub @ X727 @ (push @ (esk40_2 @ X726 @ X727) @ id)) @ id)|(~(X726 @ id @ (lam @ (esk39_2 @ X726 @ X727 @ sh @ one)) @ id)|(X726 @ id @ (lam @ (sub @ X727 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aa_lthm))&((X726 @ id @ (esk40_2 @ X726 @ X727) @ id)|(~(X726 @ id @ (lam @ (esk39_2 @ X726 @ X727 @ sh @ one)) @ id)|(X726 @ id @ (lam @ (sub @ X727 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aa_lthm))))&((~(X726 @ id @ (sub @ X727 @ (push @ (esk40_2 @ X726 @ X727) @ id)) @ id)|((X726 @ id @ (esk39_2 @ X726 @ X727 @ id @ X732) @ id)|~(X726 @ id @ X732 @ id)|(X726 @ id @ (lam @ (sub @ X727 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aa_lthm))&((X726 @ id @ (esk40_2 @ X726 @ X727) @ id)|((X726 @ id @ (esk39_2 @ X726 @ X727 @ id @ X732) @ id)|~(X726 @ id @ X732 @ id)|(X726 @ id @ (lam @ (sub @ X727 @ (push @ one @ sh))) @ id))|~(hoasinduction_lem3aa_lthm))))))&(((((((((sub @ (esk50_1 @ X734 @ X746 @ X747) @ X748)=(esk50_1 @ X734 @ (comp @ X746 @ X748) @ (sub @ X747 @ X748)))|(~(X734 @ id @ (sub @ X735 @ (push @ (esk49_2 @ X734 @ X735) @ id)) @ id)|(~(X734 @ (esk45_2 @ X734 @ X735) @ (esk46_2 @ X734 @ X735) @ (comp @ (esk48_2 @ X734 @ X735) @ (esk47_2 @ X734 @ X735)))|(X734 @ (esk41_2 @ X734 @ X735) @ (esk42_2 @ X734 @ X735) @ (comp @ (esk44_2 @ X734 @ X735) @ (esk43_2 @ X734 @ X735))))|(X734 @ id @ (lam @ X735) @ id))|~(hoasinduction_lem3))&(~(X734 @ id @ X749 @ id)|(X734 @ id @ (esk50_1 @ X734 @ id @ X749) @ id)|(~(X734 @ id @ (sub @ X735 @ (push @ (esk49_2 @ X734 @ X735) @ id)) @ id)|(~(X734 @ (esk45_2 @ X734 @ X735) @ (esk46_2 @ X734 @ X735) @ (comp @ (esk48_2 @ X734 @ X735) @ (esk47_2 @ X734 @ X735)))|(X734 @ (esk41_2 @ X734 @ X735) @ (esk42_2 @ X734 @ X735) @ (comp @ (esk44_2 @ X734 @ X735) @ 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X1242))|(epred51_0 @ id @ (esk260_1 @ X1242) @ id))|~(hoasinduction_no_psi_cond_lthm)))&(((epred52_0 @ (esk262_1 @ X1247))|(epred52_0 @ (lam @ X1247))|(((esk263_0)!=(sub @ esk263_0 @ id))|(epred9_0))|((X1242 @ (esk260_1 @ X1242))|(epred51_0 @ id @ (esk260_1 @ X1242) @ id))|~(hoasinduction_no_psi_cond_lthm))&(~(epred52_0 @ (sub @ X1247 @ (push @ (esk262_1 @ X1247) @ id)))|(epred52_0 @ (lam @ X1247))|(((esk263_0)!=(sub @ esk263_0 @ id))|(epred9_0))|((X1242 @ (esk260_1 @ X1242))|(epred51_0 @ id @ (esk260_1 @ X1242) @ id))|~(hoasinduction_no_psi_cond_lthm))))&((epred52_0 @ (ap @ X1249 @ X1250))|~(epred52_0 @ X1250)|~(epred52_0 @ X1249)|(((esk263_0)!=(sub @ esk263_0 @ id))|(epred9_0))|((X1242 @ (esk260_1 @ X1242))|(epred51_0 @ id @ (esk260_1 @ X1242) @ id))|~(hoasinduction_no_psi_cond_lthm))))&(((~(epred53_1 @ X1252 @ X1254)|(X1252 @ id @ X1254 @ id)|(hoasinduction_no_psi_cond_lthm))&(~(X1252 @ id @ X1255 @ id)|(epred53_1 @ X1252 @ X1255)|(hoasinduction_no_psi_cond_lthm)))&((((((~(X1256 @ (ap @ (esk266_1 @ X1256) @ (esk267_1 @ X1256)))|(~(X1256 @ (lam @ (esk265_1 @ X1256)))|((var @ (esk264_1 @ X1256))|(X1256 @ X1258)))|(hoasinduction_no_psi_cond_lthm))&((X1256 @ (esk267_1 @ X1256))|(~(X1256 @ (lam @ (esk265_1 @ X1256)))|((var @ (esk264_1 @ X1256))|(X1256 @ X1258)))|(hoasinduction_no_psi_cond_lthm)))&((X1256 @ (esk266_1 @ X1256))|(~(X1256 @ (lam @ (esk265_1 @ X1256)))|((var @ (esk264_1 @ X1256))|(X1256 @ X1258)))|(hoasinduction_no_psi_cond_lthm)))&(((~(X1256 @ (ap @ (esk266_1 @ X1256) @ (esk267_1 @ X1256)))|(~(X1256 @ X1260)|(X1256 @ (sub @ (esk265_1 @ X1256) @ (push @ X1260 @ id)))|((var @ (esk264_1 @ X1256))|(X1256 @ X1258)))|(hoasinduction_no_psi_cond_lthm))&((X1256 @ (esk267_1 @ X1256))|(~(X1256 @ X1260)|(X1256 @ (sub @ (esk265_1 @ X1256) @ (push @ X1260 @ id)))|((var @ (esk264_1 @ X1256))|(X1256 @ X1258)))|(hoasinduction_no_psi_cond_lthm)))&((X1256 @ (esk266_1 @ X1256))|(~(X1256 @ X1260)|(X1256 @ (sub @ (esk265_1 @ X1256) @ (push @ X1260 @ id)))|((var @ (esk264_1 @ X1256))|(X1256 @ X1258)))|(hoasinduction_no_psi_cond_lthm))))&((((~(X1256 @ (ap @ (esk266_1 @ X1256) @ (esk267_1 @ X1256)))|(~(X1256 @ (lam @ (esk265_1 @ X1256)))|(~(X1256 @ (esk264_1 @ X1256))|(X1256 @ X1258)))|(hoasinduction_no_psi_cond_lthm))&((X1256 @ (esk267_1 @ X1256))|(~(X1256 @ (lam @ (esk265_1 @ X1256)))|(~(X1256 @ (esk264_1 @ X1256))|(X1256 @ X1258)))|(hoasinduction_no_psi_cond_lthm)))&((X1256 @ (esk266_1 @ X1256))|(~(X1256 @ (lam @ (esk265_1 @ X1256)))|(~(X1256 @ (esk264_1 @ X1256))|(X1256 @ X1258)))|(hoasinduction_no_psi_cond_lthm)))&(((~(X1256 @ (ap @ (esk266_1 @ X1256) @ (esk267_1 @ X1256)))|(~(X1256 @ X1260)|(X1256 @ (sub @ (esk265_1 @ X1256) @ (push @ X1260 @ id)))|(~(X1256 @ (esk264_1 @ X1256))|(X1256 @ X1258)))|(hoasinduction_no_psi_cond_lthm))&((X1256 @ (esk267_1 @ X1256))|(~(X1256 @ X1260)|(X1256 @ (sub @ (esk265_1 @ X1256) @ (push @ X1260 @ id)))|(~(X1256 @ (esk264_1 @ X1256))|(X1256 @ X1258)))|(hoasinduction_no_psi_cond_lthm)))&((X1256 @ (esk266_1 @ X1256))|(~(X1256 @ X1260)|(X1256 @ (sub @ (esk265_1 @ X1256) @ (push @ X1260 @ id)))|(~(X1256 @ (esk264_1 @ X1256))|(X1256 @ X1258)))|(hoasinduction_no_psi_cond_lthm)))))&((((X1263)=(sub @ X1263 @ id))|(hoasinduction_no_psi_cond_lthm))&(~(epred9_0)|(hoasinduction_no_psi_cond_lthm)))))))&((~(epred12_0)|(hoasinduction_lthm))&(~(hoasinduction_lthm)|(epred12_0))))&((((sub @ esk268_0 @ (push @ (esk269_1 @ X1265) @ (esk270_1 @ X1265)))!=(X1265 @ (esk270_1 @ X1265) @ (esk269_1 @ X1265)))|(hoasinduction_lem3v2_f_lthm))&(~(hoasinduction_lem3v2_f_lthm)|((sub @ X1268 @ (push @ X1270 @ X1271))=(esk271_1 @ X1268 @ X1271 @ X1270)))))&(pushprop_lthm_orig))&(((((esk272_0)!=(esk273_0))|(hoasapinj1))&(((ap @ (sub @ esk272_0 @ id) @ esk274_0)=(ap @ (sub @ esk273_0 @ id) @ esk275_0))|(hoasapinj1)))&(~(hoasapinj1)|(((X1276)=(X1277))|((ap @ (sub @ X1276 @ id) @ X1278)!=(ap @ (sub @ X1277 @ id) @ X1279))))))&(hoasapnotvar_gthm))&(((((((var @ (esk279_3 @ X1280 @ X1281 @ X1282))|(~(X1280 @ (lam @ (esk278_3 @ X1280 @ X1281 @ X1282)))|(X1280 @ (esk277_3 @ X1280 @ X1281 @ X1282))|(X1280 @ (sub @ X1281 @ X1282)))|~(induction2lem))&(~(X1280 @ (sub @ (esk279_3 @ X1280 @ X1281 @ X1282) @ X1282))|(~(X1280 @ (lam @ (esk278_3 @ X1280 @ X1281 @ X1282)))|(X1280 @ (esk277_3 @ X1280 @ X1281 @ X1282))|(X1280 @ (sub @ X1281 @ X1282)))|~(induction2lem)))&(((var @ (esk279_3 @ X1280 @ X1281 @ X1282))|(~(X1280 @ X1286)|(X1280 @ (sub @ (esk278_3 @ X1280 @ X1281 @ X1282) @ (push @ X1286 @ id)))|(X1280 @ (esk277_3 @ X1280 @ X1281 @ X1282))|(X1280 @ (sub @ X1281 @ X1282)))|~(induction2lem))&(~(X1280 @ (sub @ (esk279_3 @ X1280 @ X1281 @ X1282) @ X1282))|(~(X1280 @ X1286)|(X1280 @ (sub @ (esk278_3 @ X1280 @ X1281 @ X1282) @ (push @ X1286 @ id)))|(X1280 @ (esk277_3 @ X1280 @ X1281 @ X1282))|(X1280 @ (sub @ X1281 @ X1282)))|~(induction2lem))))&((((var @ (esk279_3 @ X1280 @ X1281 @ X1282))|(~(X1280 @ (lam @ (esk278_3 @ X1280 @ X1281 @ X1282)))|~(X1280 @ (ap @ (esk276_3 @ X1280 @ X1281 @ X1282) @ (esk277_3 @ X1280 @ X1281 @ X1282)))|(X1280 @ (sub @ X1281 @ X1282)))|~(induction2lem))&(~(X1280 @ (sub @ (esk279_3 @ X1280 @ X1281 @ X1282) @ X1282))|(~(X1280 @ (lam @ (esk278_3 @ X1280 @ X1281 @ X1282)))|~(X1280 @ (ap @ (esk276_3 @ X1280 @ X1281 @ X1282) @ (esk277_3 @ X1280 @ X1281 @ X1282)))|(X1280 @ (sub @ X1281 @ X1282)))|~(induction2lem)))&(((var @ (esk279_3 @ X1280 @ X1281 @ X1282))|(~(X1280 @ X1286)|(X1280 @ (sub @ (esk278_3 @ X1280 @ X1281 @ X1282) @ (push @ X1286 @ id)))|~(X1280 @ (ap @ (esk276_3 @ X1280 @ X1281 @ X1282) @ (esk277_3 @ X1280 @ X1281 @ X1282)))|(X1280 @ (sub @ X1281 @ X1282)))|~(induction2lem))&(~(X1280 @ (sub @ (esk279_3 @ X1280 @ X1281 @ X1282) @ X1282))|(~(X1280 @ X1286)|(X1280 @ (sub @ (esk278_3 @ X1280 @ X1281 @ X1282) @ (push @ X1286 @ id)))|~(X1280 @ (ap @ (esk276_3 @ X1280 @ X1281 @ X1282) @ (esk277_3 @ X1280 @ X1281 @ X1282)))|(X1280 @ (sub @ X1281 @ X1282)))|~(induction2lem)))))&((((var @ (esk279_3 @ X1280 @ X1281 @ X1282))|(~(X1280 @ (lam @ (esk278_3 @ X1280 @ X1281 @ X1282)))|(X1280 @ (esk276_3 @ X1280 @ X1281 @ X1282))|(X1280 @ (sub @ X1281 @ X1282)))|~(induction2lem))&(~(X1280 @ (sub @ (esk279_3 @ X1280 @ X1281 @ X1282) @ X1282))|(~(X1280 @ (lam @ (esk278_3 @ X1280 @ X1281 @ X1282)))|(X1280 @ (esk276_3 @ X1280 @ X1281 @ X1282))|(X1280 @ (sub @ X1281 @ X1282)))|~(induction2lem)))&(((var @ (esk279_3 @ X1280 @ X1281 @ X1282))|(~(X1280 @ X1286)|(X1280 @ (sub @ (esk278_3 @ X1280 @ X1281 @ X1282) @ (push @ X1286 @ id)))|(X1280 @ (esk276_3 @ X1280 @ X1281 @ X1282))|(X1280 @ (sub @ X1281 @ X1282)))|~(induction2lem))&(~(X1280 @ (sub @ (esk279_3 @ X1280 @ X1281 @ X1282) @ X1282))|(~(X1280 @ X1286)|(X1280 @ (sub @ (esk278_3 @ X1280 @ X1281 @ X1282) @ (push @ X1286 @ id)))|(X1280 @ (esk276_3 @ X1280 @ X1281 @ X1282))|(X1280 @ (sub @ X1281 @ X1282)))|~(induction2lem)))))&((((~(epred54_0 @ X1292)|(epred54_0 @ (ap @ X1291 @ X1292))|~(epred54_0 @ X1291)|(induction2lem))&(((epred54_0 @ (esk282_1 @ X1293))|(epred54_0 @ (lam @ X1293))|(induction2lem))&(~(epred54_0 @ (sub @ X1293 @ (push @ (esk282_1 @ X1293) @ id)))|(epred54_0 @ (lam @ X1293))|(induction2lem))))&(~(epred54_0 @ (sub @ esk280_0 @ esk281_0))|(induction2lem)))&(~(var @ X1295)|(epred54_0 @ (sub @ X1295 @ esk281_0))|(induction2lem)))))&(hoasinduction_lem1v2))&(axmap))&(pushprop_lem1_gthm))&~(var @ (d2term @ d_one)))&(((~(X1297 @ X1298)|(X1296 @ id @ X1298 @ id)|~(hoasinduction_p_and_p_prime @ X1296 @ X1297))&(~(X1296 @ id @ X1299 @ id)|(X1297 @ X1299)|~(hoasinduction_p_and_p_prime @ X1296 @ X1297)))&((~(X1301 @ (esk283_2 @ X1300 @ X1301))|~(X1300 @ id @ (esk283_2 @ X1300 @ X1301) @ id)|(hoasinduction_p_and_p_prime @ X1300 @ X1301))&((X1301 @ (esk283_2 @ X1300 @ X1301))|(X1300 @ id @ (esk283_2 @ X1300 @ X1301) @ id)|(hoasinduction_p_and_p_prime @ X1300 @ X1301)))))&((hoaslam @ X1303 @ X1304)=(d2term @ d_one)))&((comp @ (d2subst @ d_id) @ (d2subst @ d_id))=(d2subst @ d_id)))&((sh)=(d2subst @ d_id)))&((id)=(d2subst @ d_id)))&((sub @ (d2term @ d_one) @ (d2subst @ d_id))=(d2term @ d_one)))&(((d2subst @ X1305)!=(d2subst @ X1306))|((X1305)=(X1306))))&((X1307)=(d_id)))&(((d2term @ X1308)!=(d2term @ X1309))|((X1308)=(X1309))))&((X1310)=(d_one)))&((X1311)=(d2term @ (esk284_1 @ X1311))))), inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])])])])])])])). 0.29/0.89 thf(c_0_13, plain, ![X2:term]:(((X2)=(d2term @ (esk284_1 @ X2)))), inference(split_conjunct,[status(thm)],[c_0_12])). 0.29/0.89 thf(c_0_14, plain, ![X77:d_term]:(((X77)=(d_one))), inference(split_conjunct,[status(thm)],[c_0_12])). 0.29/0.89 thf(c_0_15, plain, ((one)=(d2term @ d_one)), inference(split_conjunct,[status(thm)],[c_0_12])). 0.29/0.89 thf(c_0_16, negated_conjecture, ~(((pushprop_lem0)<=>![X1:term > $o, X2:term, X3:subst]:(?[X4:term > $o]:((pushprop_p_and_p_prime @ X2 @ X3 @ X1 @ X4))))), inference(assume_negation,[status(cth)],[pushprop_lem0])). 0.29/0.89 thf(c_0_17, plain, ((laminj)|((esk173_0)!=(esk174_0))), inference(split_conjunct,[status(thm)],[c_0_12])). 0.29/0.89 thf(c_0_18, plain, ![X2:term]:(((one)=(X2))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_13, c_0_14]), c_0_15])). 0.29/0.89 thf(c_0_19, negated_conjecture, ![X636:term > $o, X637:term > $o, X638:term, X639:subst]:(((~(pushprop_lem0)|~(pushprop_p_and_p_prime @ esk1_0 @ esk2_0 @ epred13_0 @ X636))&((pushprop_lem0)|(pushprop_p_and_p_prime @ X638 @ X639 @ X637 @ (epred14_3 @ X637 @ X638 @ X639))))), inference(fof_nnf,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_16])])])])])). 0.29/0.89 thf(c_0_20, plain, ![X2:term, X7:term]:((((X2)=(X7))|~((laminj))|((lam @ X2)!=(lam @ X7)))), inference(split_conjunct,[status(thm)],[c_0_12])). 0.29/0.89 thf(c_0_21, plain, (laminj), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17, c_0_18]), c_0_18])])). 0.29/0.89 thf(c_0_22, plain, ![X3:subst]:(((X3)=(d2subst @ (esk3_1 @ X3)))), inference(split_conjunct,[status(thm)],[c_0_12])). 0.29/0.89 thf(c_0_23, plain, ![X6:d_subst]:(((X6)=(d_id))), inference(split_conjunct,[status(thm)],[c_0_12])). 0.29/0.89 thf(c_0_24, plain, ((id)=(d2subst @ d_id)), inference(split_conjunct,[status(thm)],[c_0_12])). 0.29/0.89 thf(c_0_25, negated_conjecture, ![X1:term > $o]:((~((pushprop_lem0))|~((pushprop_p_and_p_prime @ esk1_0 @ esk2_0 @ epred13_0 @ X1)))), inference(split_conjunct,[status(thm)],[c_0_19])). 0.29/0.89 thf(c_0_26, plain, ![X1:term > $o]:(((pushprop_lem0)|~((X1 @ (esk105_1 @ X1)))|~((epred28_0 @ (sub @ (esk105_1 @ X1) @ (push @ esk103_0 @ esk104_0)))))), inference(split_conjunct,[status(thm)],[c_0_12])). 0.29/0.89 thf(c_0_27, plain, ![X2:term, X7:term]:(((X2)=(X7))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20, c_0_18]), c_0_18]), c_0_21])])). 0.29/0.89 thf(c_0_28, plain, ![X3:subst]:(((id)=(X3))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_22, c_0_23]), c_0_24])). 0.29/0.89 thf(c_0_29, negated_conjecture, ![X1:term > $o]:((~((pushprop_p_and_p_prime @ one @ esk2_0 @ epred13_0 @ X1))|~((pushprop_lem0)))), inference(rw,[status(thm)],[c_0_25, c_0_18])). 0.29/0.89 thf(c_0_30, plain, ![X1:term > $o]:(((X1 @ (esk105_1 @ X1))|(epred28_0 @ (sub @ (esk105_1 @ X1) @ (push @ esk103_0 @ esk104_0)))|(pushprop_lem0))), inference(split_conjunct,[status(thm)],[c_0_12])). 0.29/0.89 thf(c_0_31, plain, ((pushprop_lem0)|~((epred28_0 @ one))), inference(condense,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26, c_0_27]), c_0_27]), c_0_27]), c_0_28]), c_0_28]), c_0_18])])). 0.29/0.89 thf(c_0_32, negated_conjecture, ![X1:term > $o]:((~((pushprop_p_and_p_prime @ one @ id @ epred13_0 @ X1))|~((pushprop_lem0)))), inference(rw,[status(thm)],[c_0_29, c_0_28])). 0.29/0.89 thf(c_0_33, plain, (pushprop_lem0), inference(csr,[status(thm)],[inference(condense,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30, c_0_27]), c_0_27]), c_0_27]), c_0_28]), c_0_28]), c_0_18])]), c_0_31])). 0.29/0.89 thf(c_0_34, negated_conjecture, ![X1:term > $o]:(~((pushprop_p_and_p_prime @ one @ id @ epred13_0 @ X1))), inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_32, c_0_33])])). 0.29/0.89 thf(c_0_35, negated_conjecture, ![X3:subst, X1:term > $o]:(~((pushprop_p_and_p_prime @ one @ X3 @ epred13_0 @ X1))), inference(spm,[status(thm)],[c_0_34, c_0_28])). 0.29/0.89 thf(c_0_36, plain, ![X1:term > $o, X2:term, X4:term > $o, X3:subst]:(((pushprop_p_and_p_prime @ X2 @ X3 @ X4 @ X1)|~((X1 @ (esk4_4 @ X2 @ X3 @ X4 @ X1)))|~((X4 @ (sub @ (esk4_4 @ X2 @ X3 @ X4 @ X1) @ (push @ X2 @ X3)))))), inference(split_conjunct,[status(thm)],[c_0_12])). 0.29/0.89 thf(c_0_37, negated_conjecture, ![X3:subst, X2:term, X1:term > $o]:(~((pushprop_p_and_p_prime @ X2 @ X3 @ epred13_0 @ X1))), inference(spm,[status(thm)],[c_0_35, c_0_27])). 0.29/0.89 thf(c_0_38, plain, ![X2:term, X4:term > $o, X3:subst, X1:term > $o]:(((pushprop_p_and_p_prime @ X2 @ X3 @ X1 @ X4)|~((X4 @ one))|~((X1 @ one)))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36, c_0_27]), c_0_27]), c_0_28]), c_0_18])). 0.29/0.89 thf(c_0_39, plain, ![X2:term, X4:term > $o, X3:subst, X1:term > $o]:(((X1 @ (esk4_4 @ X2 @ X3 @ X4 @ X1))|(X4 @ (sub @ (esk4_4 @ X2 @ X3 @ X4 @ X1) @ (push @ X2 @ X3)))|(pushprop_p_and_p_prime @ X2 @ X3 @ X4 @ X1))), inference(split_conjunct,[status(thm)],[c_0_12])). 0.29/0.89 thf(c_0_40, negated_conjecture, ~((epred13_0 @ one)), inference(condense,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_38])])). 0.29/0.89 thf(c_0_41, plain, ![X2:term, X1:term > $o, X3:subst, X4:term > $o]:(((pushprop_p_and_p_prime @ X2 @ X3 @ X1 @ X4)|(X1 @ one)|(X4 @ one))), inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39, c_0_27]), c_0_27]), c_0_28]), c_0_18])). 0.29/0.89 thf(c_0_42, negated_conjecture, ![X2:term]:(~((epred13_0 @ X2))), inference(spm,[status(thm)],[c_0_40, c_0_27])). 0.29/0.89 thf(c_0_43, negated_conjecture, ($false), inference(flex_resolve,[status(thm)],[inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_37, c_0_41]), c_0_42])]), ['proof']). 0.29/0.89 % SZS output end CNFRefutation 0.29/0.89 % Parsed axioms : 132 0.29/0.89 % Removed by relevancy pruning/SinE : 0 0.29/0.89 % Initial clauses : 1373 0.29/0.89 % Removed in clause preprocessing : 130 0.29/0.89 % Initial clauses in saturation : 1243 0.29/0.89 % Processed clauses : 1498 0.29/0.89 % ...of these trivial : 779 0.29/0.89 % ...subsumed : 171 0.29/0.89 % ...remaining for further processing : 547 0.29/0.89 % Other redundant clauses eliminated : 0 0.29/0.89 % Clauses deleted for lack of memory : 0 0.29/0.89 % Backward-subsumed : 84 0.29/0.89 % Backward-rewritten : 106 0.29/0.89 % Generated clauses : 321 0.29/0.89 % ...of the previous two non-redundant : 339 0.29/0.89 % ...aggressively subsumed : 0 0.29/0.89 % Contextual simplify-reflections : 76 0.29/0.89 % Paramodulations : 321 0.29/0.89 % Factorizations : 0 0.29/0.89 % NegExts : 0 0.29/0.89 % Equation resolutions : 0 0.29/0.89 % Disequality decompositions : 0 0.29/0.89 % Total rewrite steps : 13919 0.29/0.89 % ...of those cached : 13262 0.29/0.89 % Propositional unsat checks : 0 0.29/0.89 % Propositional check models : 0 0.29/0.89 % Propositional check unsatisfiable : 0 0.29/0.89 % Propositional clauses : 0 0.29/0.89 % Propositional clauses after purity: 0 0.29/0.89 % Propositional unsat core size : 0 0.29/0.89 % Propositional preprocessing time : 0.000 0.29/0.89 % Propositional encoding time : 0.000 0.29/0.89 % Propositional solver time : 0.000 0.29/0.89 % Success case prop preproc time : 0.000 0.29/0.89 % Success case prop encoding time : 0.000 0.29/0.89 % Success case prop solver time : 0.000 0.29/0.89 % Current number of processed clauses : 164 0.29/0.89 % Positive orientable unit clauses : 103 0.29/0.89 % Positive unorientable unit clauses: 4 0.29/0.89 % Negative unit clauses : 9 0.29/0.89 % Non-unit-clauses : 48 0.29/0.89 % Current number of unprocessed clauses: 226 0.29/0.89 % ...number of literals in the above : 626 0.29/0.89 % Current number of archived formulas : 0 0.29/0.89 % Current number of archived clauses : 383 0.29/0.89 % Clause-clause subsumption calls (NU) : 20965 0.29/0.89 % Rec. Clause-clause subsumption calls : 10814 0.29/0.89 % Non-unit clause-clause subsumptions : 412 0.29/0.89 % Unit Clause-clause subsumption calls : 3148 0.29/0.89 % Rewrite failures with RHS unbound : 0 0.29/0.89 % BW rewrite match attempts : 2400 0.29/0.89 % BW rewrite match successes : 94 0.29/0.89 % Condensation attempts : 1500 0.29/0.89 % Condensation successes : 130 0.29/0.89 % Termbank termtop insertions : 150225 0.29/0.89 % Search garbage collected termcells : 24798 0.29/0.89 0.29/0.89 % ------------------------------------------------- 0.29/0.89 % User time : 0.284 s 0.29/0.89 % System time : 0.023 s 0.29/0.89 % Total time : 0.307 s 0.29/0.89 % Maximum resident set size: 8024 pages 0.29/0.89 0.29/0.89 % ------------------------------------------------- 0.29/0.89 % User time : 0.444 s 0.29/0.89 % System time : 0.042 s 0.29/0.89 % Total time : 0.486 s 0.29/0.89 % Maximum resident set size: 5376 pages 0.29/0.89 % E exiting 2.17/0.90 EOF